From aa2ca100b240cfe9601699b5939c89beb099cac2 Mon Sep 17 00:00:00 2001
From: Laurent Perrinet <laurent.perrinet@univ-amu.fr>
Date: Mon, 22 Jul 2024 11:08:13 +0200
Subject: [PATCH] going Granet

---
 2024-07-14_caustique.ipynb        | 1037 ++++++-
 2024-07-15_caustique-Granet.ipynb | 2414 +++++++++++++++
 2024-07-15_caustique-Granet.py    |  275 ++
 2024-07-15_caustique.ipynb        | 4696 +++++++++++++++++++++++++++++
 README.md                         |   19 +-
 5 files changed, 8346 insertions(+), 95 deletions(-)
 create mode 100644 2024-07-15_caustique-Granet.ipynb
 create mode 100644 2024-07-15_caustique-Granet.py
 create mode 100644 2024-07-15_caustique.ipynb

diff --git a/2024-07-14_caustique.ipynb b/2024-07-14_caustique.ipynb
index aec971d..f77455e 100644
--- a/2024-07-14_caustique.ipynb
+++ b/2024-07-14_caustique.ipynb
@@ -264,18 +264,7 @@
      "shell.execute_reply": "2022-09-16T06:50:17.664652Z"
     }
    },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "<>:181: SyntaxWarning: invalid escape sequence '\\>'\n",
-      "<>:181: SyntaxWarning: invalid escape sequence '\\>'\n",
-      "/var/folders/3p/m0g52j9j69z3gj8ktpgg1dm00000gn/T/ipykernel_72956/3587749359.py:181: SyntaxWarning: invalid escape sequence '\\>'\n",
-      "  html = HTML(f'<video {opts} src=\"{output_filename}\" type=\"video/{self.opt.ext}\" width={width}\\>')\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "import matplotlib\n",
     "import matplotlib.pyplot as plt\n",
@@ -518,15 +507,7 @@
      "shell.execute_reply": "2022-09-16T06:50:19.902008Z"
     }
    },
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "  0%|          | 0/1 [00:00<?, ?it/s]"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "c = Caustique(opt)\n",
     "output_filename = c.plot(z)"
@@ -534,7 +515,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 10,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2022-09-16T06:50:19.904998Z",
@@ -543,7 +524,20 @@
      "shell.execute_reply": "2022-09-16T06:50:19.907731Z"
     }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<img src=\"2024-07-14_caustique/caustique_ae282e1b.png\" width=\"1024\"/>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Image object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "c.show(output_filename)"
    ]
@@ -559,7 +553,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 11,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2022-09-16T06:50:19.910794Z",
@@ -585,7 +579,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 12,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
@@ -594,7 +588,23 @@
      "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
     }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "H = 10.000 -> output_filename='2024-07-14_caustique/caustique_H_10.000_ae34f7ad.png' \n",
+      "H = 11.892 -> output_filename='2024-07-14_caustique/caustique_H_11.892_b4752ed2.png' \n",
+      "H = 14.142 -> output_filename='2024-07-14_caustique/caustique_H_14.142_74ead794.png' \n",
+      "H = 16.818 -> output_filename='2024-07-14_caustique/caustique_H_16.818_8e13a8c2.png' \n",
+      "H = 20.000 -> output_filename='2024-07-14_caustique/caustique_H_20.000_8f854c6a.png' \n",
+      "H = 23.784 -> output_filename='2024-07-14_caustique/caustique_H_23.784_a7a69d8d.png' \n",
+      "H = 28.284 -> output_filename='2024-07-14_caustique/caustique_H_28.284_f2053472.png' \n",
+      "H = 33.636 -> output_filename='2024-07-14_caustique/caustique_H_33.636_d4063bd4.png' \n",
+      "H = 40.000 -> output_filename='2024-07-14_caustique/caustique_H_40.000_0f2bfcc5.png' \n"
+     ]
+    }
+   ],
    "source": [
     "for H_ in c.opt.H*np.logspace(-1, 1, N_scan, base=base):\n",
     "    opt = init()\n",
@@ -618,7 +628,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 13,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2022-09-16T06:50:21.644704Z",
@@ -627,7 +637,23 @@
      "shell.execute_reply": "2022-09-16T06:50:23.390608Z"
     }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "variation = 0.010  -> output_filename='2024-07-14_caustique/caustique_variation_0.010_2da01962.png'\n",
+      "variation = 0.017  -> output_filename='2024-07-14_caustique/caustique_variation_0.017_23fdd42d.png'\n",
+      "variation = 0.028  -> output_filename='2024-07-14_caustique/caustique_variation_0.028_0f96adeb.png'\n",
+      "variation = 0.046  -> output_filename='2024-07-14_caustique/caustique_variation_0.046_590e72b0.png'\n",
+      "variation = 0.077  -> output_filename='2024-07-14_caustique/caustique_variation_0.077_578269e5.png'\n",
+      "variation = 0.129  -> output_filename='2024-07-14_caustique/caustique_variation_0.129_27227cf5.png'\n",
+      "variation = 0.215  -> output_filename='2024-07-14_caustique/caustique_variation_0.215_dccf4840.png'\n",
+      "variation = 0.359  -> output_filename='2024-07-14_caustique/caustique_variation_0.359_ab2dfc52.png'\n",
+      "variation = 0.599  -> output_filename='2024-07-14_caustique/caustique_variation_0.599_a80b9e15.png'\n"
+     ]
+    }
+   ],
    "source": [
     "for variation_ in np.logspace(-2, 0, N_scan, base=10, endpoint=False):\n",
     "    opt = init()\n",
@@ -651,7 +677,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 14,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2022-09-16T06:50:23.394466Z",
@@ -661,7 +687,84 @@
     },
     "tags": []
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "======scale======\n",
+      "scale=scale(default)*0.500=2.560E+02 -> output_filename='2024-07-14_caustique/caustique_scale_modul_0.500_c604344d.png'\n",
+      "scale=scale(default)*0.595=3.044E+02 -> output_filename='2024-07-14_caustique/caustique_scale_modul_0.595_8a118e1b.png'\n",
+      "scale=scale(default)*0.707=3.620E+02 -> output_filename='2024-07-14_caustique/caustique_scale_modul_0.707_5127207e.png'\n",
+      "scale=scale(default)*0.841=4.305E+02 -> output_filename='2024-07-14_caustique/caustique_scale_modul_0.841_b93d1acd.png'\n",
+      "scale=scale(default)*1.000=5.120E+02 -> output_filename='2024-07-14_caustique/caustique_scale_modul_1.000_4726be6c.png'\n",
+      "scale=scale(default)*1.189=6.089E+02 -> output_filename='2024-07-14_caustique/caustique_scale_modul_1.189_efe6ea66.png'\n",
+      "scale=scale(default)*1.414=7.241E+02 -> output_filename='2024-07-14_caustique/caustique_scale_modul_1.414_37b568f3.png'\n",
+      "scale=scale(default)*1.682=8.611E+02 -> output_filename='2024-07-14_caustique/caustique_scale_modul_1.682_9931385e.png'\n",
+      "scale=scale(default)*2.000=1.024E+03 -> output_filename='2024-07-14_caustique/caustique_scale_modul_2.000_cbb3c4e4.png'\n",
+      "======B_sf======\n",
+      "B_sf=B_sf(default)*0.500=3.750E-01 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_0.500_383b4351.png'\n",
+      "B_sf=B_sf(default)*0.595=4.460E-01 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_0.595_95951377.png'\n",
+      "B_sf=B_sf(default)*0.707=5.303E-01 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_0.707_7c3540c0.png'\n",
+      "B_sf=B_sf(default)*0.841=6.307E-01 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_0.841_a9575ac6.png'\n",
+      "B_sf=B_sf(default)*1.000=7.500E-01 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_1.000_8f4e5737.png'\n",
+      "B_sf=B_sf(default)*1.189=8.919E-01 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_1.189_d2b25845.png'\n",
+      "B_sf=B_sf(default)*1.414=1.061E+00 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_1.414_2f17ce4e.png'\n",
+      "B_sf=B_sf(default)*1.682=1.261E+00 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_1.682_df4a6f79.png'\n",
+      "B_sf=B_sf(default)*2.000=1.500E+00 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_2.000_4098d1cb.png'\n",
+      "======theta======\n",
+      "theta=theta(default)*0.500=7.854E-01 -> output_filename='2024-07-14_caustique/caustique_theta_modul_0.500_242027b1.png'\n",
+      "theta=theta(default)*0.595=9.340E-01 -> output_filename='2024-07-14_caustique/caustique_theta_modul_0.595_e550294b.png'\n",
+      "theta=theta(default)*0.707=1.111E+00 -> output_filename='2024-07-14_caustique/caustique_theta_modul_0.707_7277b68e.png'\n",
+      "theta=theta(default)*0.841=1.321E+00 -> output_filename='2024-07-14_caustique/caustique_theta_modul_0.841_b73e0a2e.png'\n",
+      "theta=theta(default)*1.000=1.571E+00 -> output_filename='2024-07-14_caustique/caustique_theta_modul_1.000_cf424ffc.png'\n",
+      "theta=theta(default)*1.189=1.868E+00 -> output_filename='2024-07-14_caustique/caustique_theta_modul_1.189_7c2a3a4b.png'\n",
+      "theta=theta(default)*1.414=2.221E+00 -> output_filename='2024-07-14_caustique/caustique_theta_modul_1.414_938b2f5e.png'\n",
+      "theta=theta(default)*1.682=2.642E+00 -> output_filename='2024-07-14_caustique/caustique_theta_modul_1.682_155a3f39.png'\n",
+      "theta=theta(default)*2.000=3.142E+00 -> output_filename='2024-07-14_caustique/caustique_theta_modul_2.000_0f2224e2.png'\n",
+      "======B_theta======\n",
+      "B_theta=B_theta(default)*0.500=5.236E-01 -> output_filename='2024-07-14_caustique/caustique_B_theta_modul_0.500_b1ee37cc.png'\n",
+      "B_theta=B_theta(default)*0.595=6.227E-01 -> output_filename='2024-07-14_caustique/caustique_B_theta_modul_0.595_981305cc.png'\n",
+      "B_theta=B_theta(default)*0.707=7.405E-01 -> output_filename='2024-07-14_caustique/caustique_B_theta_modul_0.707_e6118a37.png'\n",
+      "B_theta=B_theta(default)*0.841=8.806E-01 -> output_filename='2024-07-14_caustique/caustique_B_theta_modul_0.841_a39c1030.png'\n",
+      "B_theta=B_theta(default)*1.000=1.047E+00 -> output_filename='2024-07-14_caustique/caustique_B_theta_modul_1.000_b8eab39d.png'\n",
+      "B_theta=B_theta(default)*1.189=1.245E+00 -> output_filename='2024-07-14_caustique/caustique_B_theta_modul_1.189_b4c01f0c.png'\n",
+      "B_theta=B_theta(default)*1.414=1.481E+00 -> output_filename='2024-07-14_caustique/caustique_B_theta_modul_1.414_955c5dde.png'\n",
+      "B_theta=B_theta(default)*1.682=1.761E+00 -> output_filename='2024-07-14_caustique/caustique_B_theta_modul_1.682_d79ba197.png'\n",
+      "B_theta=B_theta(default)*2.000=2.094E+00 -> output_filename='2024-07-14_caustique/caustique_B_theta_modul_2.000_f7453e38.png'\n",
+      "======gamma======\n",
+      "gamma=gamma(default)*0.500=1.450E+00 -> output_filename='2024-07-14_caustique/caustique_gamma_modul_0.500_ba6d5d7c.png'\n",
+      "gamma=gamma(default)*0.595=1.724E+00 -> output_filename='2024-07-14_caustique/caustique_gamma_modul_0.595_943b676e.png'\n",
+      "gamma=gamma(default)*0.707=2.051E+00 -> output_filename='2024-07-14_caustique/caustique_gamma_modul_0.707_2a4d88b2.png'\n",
+      "gamma=gamma(default)*0.841=2.439E+00 -> output_filename='2024-07-14_caustique/caustique_gamma_modul_0.841_8449735a.png'\n",
+      "gamma=gamma(default)*1.000=2.900E+00 -> output_filename='2024-07-14_caustique/caustique_gamma_modul_1.000_9dda329f.png'\n",
+      "gamma=gamma(default)*1.189=3.449E+00 -> output_filename='2024-07-14_caustique/caustique_gamma_modul_1.189_76347b5f.png'\n",
+      "gamma=gamma(default)*1.414=4.101E+00 -> output_filename='2024-07-14_caustique/caustique_gamma_modul_1.414_e416938f.png'\n",
+      "gamma=gamma(default)*1.682=4.877E+00 -> output_filename='2024-07-14_caustique/caustique_gamma_modul_1.682_e1a4096e.png'\n",
+      "gamma=gamma(default)*2.000=5.800E+00 -> output_filename='2024-07-14_caustique/caustique_gamma_modul_2.000_a89910d3.png'\n",
+      "======min_lum======\n",
+      "min_lum=min_lum(default)*0.500=5.000E-02 -> output_filename='2024-07-14_caustique/caustique_min_lum_modul_0.500_78f7d01a.png'\n",
+      "min_lum=min_lum(default)*0.595=5.946E-02 -> output_filename='2024-07-14_caustique/caustique_min_lum_modul_0.595_f4033056.png'\n",
+      "min_lum=min_lum(default)*0.707=7.071E-02 -> output_filename='2024-07-14_caustique/caustique_min_lum_modul_0.707_e8313869.png'\n",
+      "min_lum=min_lum(default)*0.841=8.409E-02 -> output_filename='2024-07-14_caustique/caustique_min_lum_modul_0.841_ec324732.png'\n",
+      "min_lum=min_lum(default)*1.000=1.000E-01 -> output_filename='2024-07-14_caustique/caustique_min_lum_modul_1.000_12d0eee9.png'\n",
+      "min_lum=min_lum(default)*1.189=1.189E-01 -> output_filename='2024-07-14_caustique/caustique_min_lum_modul_1.189_059343b5.png'\n",
+      "min_lum=min_lum(default)*1.414=1.414E-01 -> output_filename='2024-07-14_caustique/caustique_min_lum_modul_1.414_c48ebc27.png'\n",
+      "min_lum=min_lum(default)*1.682=1.682E-01 -> output_filename='2024-07-14_caustique/caustique_min_lum_modul_1.682_497c3bfd.png'\n",
+      "min_lum=min_lum(default)*2.000=2.000E-01 -> output_filename='2024-07-14_caustique/caustique_min_lum_modul_2.000_2ec2ab1f.png'\n",
+      "======zmin======\n",
+      "zmin=zmin(default)*0.500=1.000E-01 -> output_filename='2024-07-14_caustique/caustique_zmin_modul_0.500_76289697.png'\n",
+      "zmin=zmin(default)*0.595=1.189E-01 -> output_filename='2024-07-14_caustique/caustique_zmin_modul_0.595_384a4243.png'\n",
+      "zmin=zmin(default)*0.707=1.414E-01 -> output_filename='2024-07-14_caustique/caustique_zmin_modul_0.707_1f61d862.png'\n",
+      "zmin=zmin(default)*0.841=1.682E-01 -> output_filename='2024-07-14_caustique/caustique_zmin_modul_0.841_d2a0b0c9.png'\n",
+      "zmin=zmin(default)*1.000=2.000E-01 -> output_filename='2024-07-14_caustique/caustique_zmin_modul_1.000_5ce3c1db.png'\n",
+      "zmin=zmin(default)*1.189=2.378E-01 -> output_filename='2024-07-14_caustique/caustique_zmin_modul_1.189_10d93ccb.png'\n",
+      "zmin=zmin(default)*1.414=2.828E-01 -> output_filename='2024-07-14_caustique/caustique_zmin_modul_1.414_2d132a18.png'\n",
+      "zmin=zmin(default)*1.682=3.364E-01 -> output_filename='2024-07-14_caustique/caustique_zmin_modul_1.682_7e5ce573.png'\n",
+      "zmin=zmin(default)*2.000=4.000E-01 -> output_filename='2024-07-14_caustique/caustique_zmin_modul_2.000_a27f6770.png'\n"
+     ]
+    }
+   ],
    "source": [
     "for variable in ['scale', 'B_sf', 'theta',  'B_theta', 'gamma', 'min_lum', 'zmin']: #  'V_Y', 'V_X', 'B_V', \n",
     "    print(f'======{variable}======')\n",
@@ -686,7 +789,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 15,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -695,9 +798,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 16,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "def generate_image(nx, ny, periods=6.25, threshold=0.45, radius=.9):\n",
     "    X, Y = np.meshgrid(np.linspace(-1, 1, nx, endpoint=True), np.linspace(-1, 1, ny, endpoint=True))\n",
@@ -712,9 +826,22 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 17,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<img src=\"2024-07-14_caustique/caustique_grating-image_0f4d6abd.png\" width=\"1024\"/>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Image object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "c = Caustique(init())\n",
     "c.opt.tag = f'{c.opt.tag}_{type}-image'\n",
@@ -724,9 +851,25 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 18,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "H = 10.000 -> output_filename='2024-07-14_caustique/caustique_grating-image_H_10.000_ad40f238.png' \n",
+      "H = 11.892 -> output_filename='2024-07-14_caustique/caustique_grating-image_H_11.892_74cee302.png' \n",
+      "H = 14.142 -> output_filename='2024-07-14_caustique/caustique_grating-image_H_14.142_a7a1b4de.png' \n",
+      "H = 16.818 -> output_filename='2024-07-14_caustique/caustique_grating-image_H_16.818_403d723f.png' \n",
+      "H = 20.000 -> output_filename='2024-07-14_caustique/caustique_grating-image_H_20.000_ea3ebcb9.png' \n",
+      "H = 23.784 -> output_filename='2024-07-14_caustique/caustique_grating-image_H_23.784_8d4ecd03.png' \n",
+      "H = 28.284 -> output_filename='2024-07-14_caustique/caustique_grating-image_H_28.284_ee4904bf.png' \n",
+      "H = 33.636 -> output_filename='2024-07-14_caustique/caustique_grating-image_H_33.636_dee9e852.png' \n",
+      "H = 40.000 -> output_filename='2024-07-14_caustique/caustique_grating-image_H_40.000_1e5e805b.png' \n"
+     ]
+    }
+   ],
    "source": [
     "for H_ in c.opt.H*np.logspace(-1, 1, N_scan, base=base):\n",
     "    opt = init()\n",
@@ -741,9 +884,25 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 19,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.100 -> output_filename='2024-07-14_caustique/caustique_grating-image_threshold=0.100_a3c1b385.png' \n",
+      "0.200 -> output_filename='2024-07-14_caustique/caustique_grating-image_threshold=0.200_4e55756a.png' \n",
+      "0.300 -> output_filename='2024-07-14_caustique/caustique_grating-image_threshold=0.300_d1092b03.png' \n",
+      "0.400 -> output_filename='2024-07-14_caustique/caustique_grating-image_threshold=0.400_992d2572.png' \n",
+      "0.500 -> output_filename='2024-07-14_caustique/caustique_grating-image_threshold=0.500_0dc18b43.png' \n",
+      "0.600 -> output_filename='2024-07-14_caustique/caustique_grating-image_threshold=0.600_5a21681f.png' \n",
+      "0.700 -> output_filename='2024-07-14_caustique/caustique_grating-image_threshold=0.700_0c00edac.png' \n",
+      "0.800 -> output_filename='2024-07-14_caustique/caustique_grating-image_threshold=0.800_3043c558.png' \n",
+      "0.900 -> output_filename='2024-07-14_caustique/caustique_grating-image_threshold=0.900_ff5af108.png' \n"
+     ]
+    }
+   ],
    "source": [
     "for threshold in np.linspace(0, 1, N_scan+2, endpoint=True)[1:-1]:\n",
     "    opt = init()\n",
@@ -758,9 +917,25 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 20,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "radius=0.111 -> output_filename='2024-07-14_caustique/caustique_grating-image_radius=0.111_506f42be.png' \n",
+      "radius=0.222 -> output_filename='2024-07-14_caustique/caustique_grating-image_radius=0.222_2093ce00.png' \n",
+      "radius=0.333 -> output_filename='2024-07-14_caustique/caustique_grating-image_radius=0.333_2c311f7e.png' \n",
+      "radius=0.444 -> output_filename='2024-07-14_caustique/caustique_grating-image_radius=0.444_f2cc585a.png' \n",
+      "radius=0.556 -> output_filename='2024-07-14_caustique/caustique_grating-image_radius=0.556_02219953.png' \n",
+      "radius=0.667 -> output_filename='2024-07-14_caustique/caustique_grating-image_radius=0.667_8abb8845.png' \n",
+      "radius=0.778 -> output_filename='2024-07-14_caustique/caustique_grating-image_radius=0.778_8069def4.png' \n",
+      "radius=0.889 -> output_filename='2024-07-14_caustique/caustique_grating-image_radius=0.889_8490256a.png' \n",
+      "radius=1.000 -> output_filename='2024-07-14_caustique/caustique_grating-image_radius=1.000_17e95f27.png' \n"
+     ]
+    }
+   ],
    "source": [
     "for radius in np.linspace(0, 1, N_scan+1)[1:]:\n",
     "    opt = init()\n",
@@ -775,9 +950,25 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 21,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "periods=1.000 -> output_filename='2024-07-14_caustique/caustique_grating-image_periods=1.00e+00_398f3b6a.png' \n",
+      "periods=1.334 -> output_filename='2024-07-14_caustique/caustique_grating-image_periods=1.33e+00_ead8222a.png' \n",
+      "periods=1.778 -> output_filename='2024-07-14_caustique/caustique_grating-image_periods=1.78e+00_e5410dfb.png' \n",
+      "periods=2.371 -> output_filename='2024-07-14_caustique/caustique_grating-image_periods=2.37e+00_b922972a.png' \n",
+      "periods=3.162 -> output_filename='2024-07-14_caustique/caustique_grating-image_periods=3.16e+00_620eccdf.png' \n",
+      "periods=4.217 -> output_filename='2024-07-14_caustique/caustique_grating-image_periods=4.22e+00_599aff90.png' \n",
+      "periods=5.623 -> output_filename='2024-07-14_caustique/caustique_grating-image_periods=5.62e+00_e09f7302.png' \n",
+      "periods=7.499 -> output_filename='2024-07-14_caustique/caustique_grating-image_periods=7.50e+00_b3344e7c.png' \n",
+      "periods=10.000 -> output_filename='2024-07-14_caustique/caustique_grating-image_periods=1.00e+01_248ef1c2.png' \n"
+     ]
+    }
+   ],
    "source": [
     "for periods in np.logspace(0, 1, N_scan, base=10):\n",
     "    opt = init()\n",
@@ -790,6 +981,103 @@
     "    if c.opt.do_display: c.show(output_filename)"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "======scale======\n",
+      "scale=scale(default)*0.500=2.560E+02 -> output_filename='2024-07-14_caustique/caustique_scale_modul_0.500_c604344d.png'\n",
+      "scale=scale(default)*0.595=3.044E+02 -> output_filename='2024-07-14_caustique/caustique_scale_modul_0.595_8a118e1b.png'\n",
+      "scale=scale(default)*0.707=3.620E+02 -> output_filename='2024-07-14_caustique/caustique_scale_modul_0.707_5127207e.png'\n",
+      "scale=scale(default)*0.841=4.305E+02 -> output_filename='2024-07-14_caustique/caustique_scale_modul_0.841_b93d1acd.png'\n",
+      "scale=scale(default)*1.000=5.120E+02 -> output_filename='2024-07-14_caustique/caustique_scale_modul_1.000_4726be6c.png'\n",
+      "scale=scale(default)*1.189=6.089E+02 -> output_filename='2024-07-14_caustique/caustique_scale_modul_1.189_efe6ea66.png'\n",
+      "scale=scale(default)*1.414=7.241E+02 -> output_filename='2024-07-14_caustique/caustique_scale_modul_1.414_37b568f3.png'\n",
+      "scale=scale(default)*1.682=8.611E+02 -> output_filename='2024-07-14_caustique/caustique_scale_modul_1.682_9931385e.png'\n",
+      "scale=scale(default)*2.000=1.024E+03 -> output_filename='2024-07-14_caustique/caustique_scale_modul_2.000_cbb3c4e4.png'\n",
+      "======B_sf======\n",
+      "B_sf=B_sf(default)*0.500=3.750E-01 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_0.500_383b4351.png'\n",
+      "B_sf=B_sf(default)*0.595=4.460E-01 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_0.595_95951377.png'\n",
+      "B_sf=B_sf(default)*0.707=5.303E-01 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_0.707_7c3540c0.png'\n",
+      "B_sf=B_sf(default)*0.841=6.307E-01 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_0.841_a9575ac6.png'\n",
+      "B_sf=B_sf(default)*1.000=7.500E-01 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_1.000_8f4e5737.png'\n",
+      "B_sf=B_sf(default)*1.189=8.919E-01 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_1.189_d2b25845.png'\n",
+      "B_sf=B_sf(default)*1.414=1.061E+00 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_1.414_2f17ce4e.png'\n",
+      "B_sf=B_sf(default)*1.682=1.261E+00 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_1.682_df4a6f79.png'\n",
+      "B_sf=B_sf(default)*2.000=1.500E+00 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_2.000_4098d1cb.png'\n",
+      "======theta======\n",
+      "theta=theta(default)*0.500=7.854E-01 -> output_filename='2024-07-14_caustique/caustique_theta_modul_0.500_242027b1.png'\n",
+      "theta=theta(default)*0.595=9.340E-01 -> output_filename='2024-07-14_caustique/caustique_theta_modul_0.595_e550294b.png'\n",
+      "theta=theta(default)*0.707=1.111E+00 -> output_filename='2024-07-14_caustique/caustique_theta_modul_0.707_7277b68e.png'\n",
+      "theta=theta(default)*0.841=1.321E+00 -> output_filename='2024-07-14_caustique/caustique_theta_modul_0.841_b73e0a2e.png'\n",
+      "theta=theta(default)*1.000=1.571E+00 -> output_filename='2024-07-14_caustique/caustique_theta_modul_1.000_cf424ffc.png'\n",
+      "theta=theta(default)*1.189=1.868E+00 -> output_filename='2024-07-14_caustique/caustique_theta_modul_1.189_7c2a3a4b.png'\n",
+      "theta=theta(default)*1.414=2.221E+00 -> output_filename='2024-07-14_caustique/caustique_theta_modul_1.414_938b2f5e.png'\n",
+      "theta=theta(default)*1.682=2.642E+00 -> output_filename='2024-07-14_caustique/caustique_theta_modul_1.682_155a3f39.png'\n",
+      "theta=theta(default)*2.000=3.142E+00 -> output_filename='2024-07-14_caustique/caustique_theta_modul_2.000_0f2224e2.png'\n",
+      "======B_theta======\n",
+      "B_theta=B_theta(default)*0.500=5.236E-01 -> output_filename='2024-07-14_caustique/caustique_B_theta_modul_0.500_b1ee37cc.png'\n",
+      "B_theta=B_theta(default)*0.595=6.227E-01 -> output_filename='2024-07-14_caustique/caustique_B_theta_modul_0.595_981305cc.png'\n",
+      "B_theta=B_theta(default)*0.707=7.405E-01 -> output_filename='2024-07-14_caustique/caustique_B_theta_modul_0.707_e6118a37.png'\n",
+      "B_theta=B_theta(default)*0.841=8.806E-01 -> output_filename='2024-07-14_caustique/caustique_B_theta_modul_0.841_a39c1030.png'\n",
+      "B_theta=B_theta(default)*1.000=1.047E+00 -> output_filename='2024-07-14_caustique/caustique_B_theta_modul_1.000_b8eab39d.png'\n",
+      "B_theta=B_theta(default)*1.189=1.245E+00 -> output_filename='2024-07-14_caustique/caustique_B_theta_modul_1.189_b4c01f0c.png'\n",
+      "B_theta=B_theta(default)*1.414=1.481E+00 -> output_filename='2024-07-14_caustique/caustique_B_theta_modul_1.414_955c5dde.png'\n",
+      "B_theta=B_theta(default)*1.682=1.761E+00 -> output_filename='2024-07-14_caustique/caustique_B_theta_modul_1.682_d79ba197.png'\n",
+      "B_theta=B_theta(default)*2.000=2.094E+00 -> output_filename='2024-07-14_caustique/caustique_B_theta_modul_2.000_f7453e38.png'\n",
+      "======gamma======\n",
+      "gamma=gamma(default)*0.500=1.450E+00 -> output_filename='2024-07-14_caustique/caustique_gamma_modul_0.500_ba6d5d7c.png'\n",
+      "gamma=gamma(default)*0.595=1.724E+00 -> output_filename='2024-07-14_caustique/caustique_gamma_modul_0.595_943b676e.png'\n",
+      "gamma=gamma(default)*0.707=2.051E+00 -> output_filename='2024-07-14_caustique/caustique_gamma_modul_0.707_2a4d88b2.png'\n",
+      "gamma=gamma(default)*0.841=2.439E+00 -> output_filename='2024-07-14_caustique/caustique_gamma_modul_0.841_8449735a.png'\n",
+      "gamma=gamma(default)*1.000=2.900E+00 -> output_filename='2024-07-14_caustique/caustique_gamma_modul_1.000_9dda329f.png'\n",
+      "gamma=gamma(default)*1.189=3.449E+00 -> output_filename='2024-07-14_caustique/caustique_gamma_modul_1.189_76347b5f.png'\n",
+      "gamma=gamma(default)*1.414=4.101E+00 -> output_filename='2024-07-14_caustique/caustique_gamma_modul_1.414_e416938f.png'\n",
+      "gamma=gamma(default)*1.682=4.877E+00 -> output_filename='2024-07-14_caustique/caustique_gamma_modul_1.682_e1a4096e.png'\n",
+      "gamma=gamma(default)*2.000=5.800E+00 -> output_filename='2024-07-14_caustique/caustique_gamma_modul_2.000_a89910d3.png'\n",
+      "======min_lum======\n",
+      "min_lum=min_lum(default)*0.500=5.000E-02 -> output_filename='2024-07-14_caustique/caustique_min_lum_modul_0.500_78f7d01a.png'\n",
+      "min_lum=min_lum(default)*0.595=5.946E-02 -> output_filename='2024-07-14_caustique/caustique_min_lum_modul_0.595_f4033056.png'\n",
+      "min_lum=min_lum(default)*0.707=7.071E-02 -> output_filename='2024-07-14_caustique/caustique_min_lum_modul_0.707_e8313869.png'\n",
+      "min_lum=min_lum(default)*0.841=8.409E-02 -> output_filename='2024-07-14_caustique/caustique_min_lum_modul_0.841_ec324732.png'\n",
+      "min_lum=min_lum(default)*1.000=1.000E-01 -> output_filename='2024-07-14_caustique/caustique_min_lum_modul_1.000_12d0eee9.png'\n",
+      "min_lum=min_lum(default)*1.189=1.189E-01 -> output_filename='2024-07-14_caustique/caustique_min_lum_modul_1.189_059343b5.png'\n",
+      "min_lum=min_lum(default)*1.414=1.414E-01 -> output_filename='2024-07-14_caustique/caustique_min_lum_modul_1.414_c48ebc27.png'\n",
+      "min_lum=min_lum(default)*1.682=1.682E-01 -> output_filename='2024-07-14_caustique/caustique_min_lum_modul_1.682_497c3bfd.png'\n",
+      "min_lum=min_lum(default)*2.000=2.000E-01 -> output_filename='2024-07-14_caustique/caustique_min_lum_modul_2.000_2ec2ab1f.png'\n",
+      "======zmin======\n",
+      "zmin=zmin(default)*0.500=1.000E-01 -> output_filename='2024-07-14_caustique/caustique_zmin_modul_0.500_76289697.png'\n",
+      "zmin=zmin(default)*0.595=1.189E-01 -> output_filename='2024-07-14_caustique/caustique_zmin_modul_0.595_384a4243.png'\n",
+      "zmin=zmin(default)*0.707=1.414E-01 -> output_filename='2024-07-14_caustique/caustique_zmin_modul_0.707_1f61d862.png'\n",
+      "zmin=zmin(default)*0.841=1.682E-01 -> output_filename='2024-07-14_caustique/caustique_zmin_modul_0.841_d2a0b0c9.png'\n",
+      "zmin=zmin(default)*1.000=2.000E-01 -> output_filename='2024-07-14_caustique/caustique_zmin_modul_1.000_5ce3c1db.png'\n",
+      "zmin=zmin(default)*1.189=2.378E-01 -> output_filename='2024-07-14_caustique/caustique_zmin_modul_1.189_10d93ccb.png'\n",
+      "zmin=zmin(default)*1.414=2.828E-01 -> output_filename='2024-07-14_caustique/caustique_zmin_modul_1.414_2d132a18.png'\n",
+      "zmin=zmin(default)*1.682=3.364E-01 -> output_filename='2024-07-14_caustique/caustique_zmin_modul_1.682_7e5ce573.png'\n",
+      "zmin=zmin(default)*2.000=4.000E-01 -> output_filename='2024-07-14_caustique/caustique_zmin_modul_2.000_a27f6770.png'\n"
+     ]
+    }
+   ],
+   "source": [
+    "for variable in ['scale', 'B_sf', 'theta',  'B_theta', 'gamma', 'min_lum', 'zmin']: #  'V_Y', 'V_X', 'B_V', \n",
+    "    print(f'======{variable}======')\n",
+    "    for modul in np.logspace(-1, 1, N_scan, base=base):\n",
+    "        opt = init()\n",
+    "        c = Caustique(opt)\n",
+    "        c.d[variable] *= modul\n",
+    "        c.opt.tag = f'{c.opt.tag}_{variable}_modul_{modul:.3f}'\n",
+    "        z = c.wave()\n",
+    "        image = generate_image(nx=c.opt.nx, ny=c.opt.ny)\n",
+    "        output_filename = c.plot(z, image)\n",
+    "        print(f'{variable}={variable}(default)*{modul:.3f}={c.d[variable]:.3E} -> {output_filename=}')\n",
+    "        if c.opt.do_display: c.show(output_filename)"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {
@@ -801,7 +1089,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 23,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -810,9 +1098,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 24,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "def generate_image(nx, ny, periods=10, threshold=0.45, radius=.9):\n",
     "    X, Y = np.meshgrid(np.linspace(-1, 1, nx, endpoint=True), np.linspace(-1, 1, ny, endpoint=True))\n",
@@ -828,9 +1127,22 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 25,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<img src=\"2024-07-14_caustique/caustique_grid-image_3b042836.png\" width=\"1024\"/>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Image object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "c = Caustique(init())\n",
     "c.opt.tag = f'{c.opt.tag}_{type}-image'\n",
@@ -841,7 +1153,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 26,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
@@ -850,7 +1162,23 @@
      "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
     }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "threshold=0.100 -> output_filename='2024-07-14_caustique/caustique_grid-image_threshold=0.100_d3898cb2.png' \n",
+      "threshold=0.200 -> output_filename='2024-07-14_caustique/caustique_grid-image_threshold=0.200_d725e91c.png' \n",
+      "threshold=0.300 -> output_filename='2024-07-14_caustique/caustique_grid-image_threshold=0.300_69d58422.png' \n",
+      "threshold=0.400 -> output_filename='2024-07-14_caustique/caustique_grid-image_threshold=0.400_33b6ec67.png' \n",
+      "threshold=0.500 -> output_filename='2024-07-14_caustique/caustique_grid-image_threshold=0.500_876672bd.png' \n",
+      "threshold=0.600 -> output_filename='2024-07-14_caustique/caustique_grid-image_threshold=0.600_8284a303.png' \n",
+      "threshold=0.700 -> output_filename='2024-07-14_caustique/caustique_grid-image_threshold=0.700_8e369d08.png' \n",
+      "threshold=0.800 -> output_filename='2024-07-14_caustique/caustique_grid-image_threshold=0.800_0e3a91a8.png' \n",
+      "threshold=0.900 -> output_filename='2024-07-14_caustique/caustique_grid-image_threshold=0.900_c2317ac6.png' \n"
+     ]
+    }
+   ],
    "source": [
     "for threshold in np.linspace(0, 1, N_scan+2, endpoint=True)[1:-1]:\n",
     "    opt = init()\n",
@@ -865,7 +1193,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 27,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
@@ -874,7 +1202,23 @@
      "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
     }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "H = 10.000 -> output_filename='2024-07-14_caustique/caustique_grid-image_H_10.000_ee4aa4eb.png' \n",
+      "H = 11.892 -> output_filename='2024-07-14_caustique/caustique_grid-image_H_11.892_3ed2289e.png' \n",
+      "H = 14.142 -> output_filename='2024-07-14_caustique/caustique_grid-image_H_14.142_671eaed7.png' \n",
+      "H = 16.818 -> output_filename='2024-07-14_caustique/caustique_grid-image_H_16.818_93af91ea.png' \n",
+      "H = 20.000 -> output_filename='2024-07-14_caustique/caustique_grid-image_H_20.000_ea2a5518.png' \n",
+      "H = 23.784 -> output_filename='2024-07-14_caustique/caustique_grid-image_H_23.784_d1747c22.png' \n",
+      "H = 28.284 -> output_filename='2024-07-14_caustique/caustique_grid-image_H_28.284_09e14169.png' \n",
+      "H = 33.636 -> output_filename='2024-07-14_caustique/caustique_grid-image_H_33.636_6146eac8.png' \n",
+      "H = 40.000 -> output_filename='2024-07-14_caustique/caustique_grid-image_H_40.000_4da793a1.png' \n"
+     ]
+    }
+   ],
    "source": [
     "for H_ in c.opt.H*np.logspace(-1, 1, N_scan, base=base):\n",
     "    opt = init()\n",
@@ -889,7 +1233,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 28,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
@@ -898,7 +1242,23 @@
      "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
     }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "periods=1.000 -> output_filename='2024-07-14_caustique/caustique_grid-image_periods=1.000_31de32b4.png' \n",
+      "periods=1.334 -> output_filename='2024-07-14_caustique/caustique_grid-image_periods=1.334_d47dd95c.png' \n",
+      "periods=1.778 -> output_filename='2024-07-14_caustique/caustique_grid-image_periods=1.778_69b38a9d.png' \n",
+      "periods=2.371 -> output_filename='2024-07-14_caustique/caustique_grid-image_periods=2.371_56d7fff7.png' \n",
+      "periods=3.162 -> output_filename='2024-07-14_caustique/caustique_grid-image_periods=3.162_625ad5df.png' \n",
+      "periods=4.217 -> output_filename='2024-07-14_caustique/caustique_grid-image_periods=4.217_4e0b51a7.png' \n",
+      "periods=5.623 -> output_filename='2024-07-14_caustique/caustique_grid-image_periods=5.623_7fd080aa.png' \n",
+      "periods=7.499 -> output_filename='2024-07-14_caustique/caustique_grid-image_periods=7.499_abf0d88a.png' \n",
+      "periods=10.000 -> output_filename='2024-07-14_caustique/caustique_grid-image_periods=10.000_62096666.png' \n"
+     ]
+    }
+   ],
    "source": [
     "for periods in np.logspace(0, 1, N_scan, base=10):\n",
     "    opt = init()\n",
@@ -922,7 +1282,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 29,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -931,9 +1291,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 30,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "def generate_image(nx, ny, periods=6.5, threshold=0.45, radius=.9):\n",
     "    X, Y = np.meshgrid(np.linspace(-1, 1, nx, endpoint=True), np.linspace(-1, 1, ny, endpoint=True))\n",
@@ -948,9 +1319,22 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 31,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<img src=\"2024-07-14_caustique/caustique_hole-image_9b4d2f3e.png\" width=\"1024\"/>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Image object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "c = Caustique(init())\n",
     "c.opt.tag = f'{c.opt.tag}_{type}-image'\n",
@@ -961,7 +1345,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 32,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
@@ -970,7 +1354,23 @@
      "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
     }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "H = 10.000 -> output_filename='2024-07-14_caustique/caustique_hole-image_H_10.000_ed7ca120.png' \n",
+      "H = 11.892 -> output_filename='2024-07-14_caustique/caustique_hole-image_H_11.892_ba2ac289.png' \n",
+      "H = 14.142 -> output_filename='2024-07-14_caustique/caustique_hole-image_H_14.142_a39fd2e5.png' \n",
+      "H = 16.818 -> output_filename='2024-07-14_caustique/caustique_hole-image_H_16.818_8b7fd1d1.png' \n",
+      "H = 20.000 -> output_filename='2024-07-14_caustique/caustique_hole-image_H_20.000_909186ef.png' \n",
+      "H = 23.784 -> output_filename='2024-07-14_caustique/caustique_hole-image_H_23.784_71395bee.png' \n",
+      "H = 28.284 -> output_filename='2024-07-14_caustique/caustique_hole-image_H_28.284_738e7644.png' \n",
+      "H = 33.636 -> output_filename='2024-07-14_caustique/caustique_hole-image_H_33.636_588d4492.png' \n",
+      "H = 40.000 -> output_filename='2024-07-14_caustique/caustique_hole-image_H_40.000_7e52add3.png' \n"
+     ]
+    }
+   ],
    "source": [
     "for H_ in c.opt.H*np.logspace(-1, 1, N_scan, base=base):\n",
     "    opt = init()\n",
@@ -985,7 +1385,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 33,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
@@ -994,7 +1394,23 @@
      "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
     }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "threshold=0.100 -> output_filename='2024-07-14_caustique/caustique_hole-image_threshold=0.100_e0d53e21.png' \n",
+      "threshold=0.200 -> output_filename='2024-07-14_caustique/caustique_hole-image_threshold=0.200_d43c8b6d.png' \n",
+      "threshold=0.300 -> output_filename='2024-07-14_caustique/caustique_hole-image_threshold=0.300_a4cc1983.png' \n",
+      "threshold=0.400 -> output_filename='2024-07-14_caustique/caustique_hole-image_threshold=0.400_37a4b140.png' \n",
+      "threshold=0.500 -> output_filename='2024-07-14_caustique/caustique_hole-image_threshold=0.500_e7001ca6.png' \n",
+      "threshold=0.600 -> output_filename='2024-07-14_caustique/caustique_hole-image_threshold=0.600_c46451fc.png' \n",
+      "threshold=0.700 -> output_filename='2024-07-14_caustique/caustique_hole-image_threshold=0.700_b9e5f689.png' \n",
+      "threshold=0.800 -> output_filename='2024-07-14_caustique/caustique_hole-image_threshold=0.800_8e55b3d4.png' \n",
+      "threshold=0.900 -> output_filename='2024-07-14_caustique/caustique_hole-image_threshold=0.900_ba85d5b7.png' \n"
+     ]
+    }
+   ],
    "source": [
     "for threshold in np.linspace(0, 1, N_scan+2, endpoint=True)[1:-1]:\n",
     "    opt = init()\n",
@@ -1009,7 +1425,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 34,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
@@ -1018,7 +1434,23 @@
      "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
     }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "periods=1.000 -> output_filename='2024-07-14_caustique/caustique_hole-image_periods=1.000_5d4213e7.png' \n",
+      "periods=1.334 -> output_filename='2024-07-14_caustique/caustique_hole-image_periods=1.334_5f014d84.png' \n",
+      "periods=1.778 -> output_filename='2024-07-14_caustique/caustique_hole-image_periods=1.778_bc297376.png' \n",
+      "periods=2.371 -> output_filename='2024-07-14_caustique/caustique_hole-image_periods=2.371_d4bb5cf6.png' \n",
+      "periods=3.162 -> output_filename='2024-07-14_caustique/caustique_hole-image_periods=3.162_8f04bd17.png' \n",
+      "periods=4.217 -> output_filename='2024-07-14_caustique/caustique_hole-image_periods=4.217_7cf8e0de.png' \n",
+      "periods=5.623 -> output_filename='2024-07-14_caustique/caustique_hole-image_periods=5.623_6c912984.png' \n",
+      "periods=7.499 -> output_filename='2024-07-14_caustique/caustique_hole-image_periods=7.499_08e4064f.png' \n",
+      "periods=10.000 -> output_filename='2024-07-14_caustique/caustique_hole-image_periods=10.000_da1a7415.png' \n"
+     ]
+    }
+   ],
    "source": [
     "for periods in np.logspace(0, 1, N_scan, base=10):\n",
     "    opt = init()\n",
@@ -1042,7 +1474,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 35,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1051,9 +1483,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 36,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "def generate_image(nx, ny,  radius=.9):\n",
     "    X, Y = np.meshgrid(np.linspace(-1, 1, nx, endpoint=True), np.linspace(-1, 1, ny, endpoint=True))\n",
@@ -1065,9 +1508,22 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 37,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<img src=\"2024-07-14_caustique/caustique_square-image_831afd95.png\" width=\"1024\"/>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Image object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "c = Caustique(init())\n",
     "c.opt.tag = f'{c.opt.tag}_{type}-image'\n",
@@ -1077,7 +1533,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 38,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
@@ -1086,7 +1542,23 @@
      "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
     }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "H = 10.000 -> output_filename='2024-07-14_caustique/caustique_square-image_H_10.000_29fdea66.png' \n",
+      "H = 11.892 -> output_filename='2024-07-14_caustique/caustique_square-image_H_11.892_f877ae42.png' \n",
+      "H = 14.142 -> output_filename='2024-07-14_caustique/caustique_square-image_H_14.142_c236fda9.png' \n",
+      "H = 16.818 -> output_filename='2024-07-14_caustique/caustique_square-image_H_16.818_5ded8ca9.png' \n",
+      "H = 20.000 -> output_filename='2024-07-14_caustique/caustique_square-image_H_20.000_463674a3.png' \n",
+      "H = 23.784 -> output_filename='2024-07-14_caustique/caustique_square-image_H_23.784_bf2d15b7.png' \n",
+      "H = 28.284 -> output_filename='2024-07-14_caustique/caustique_square-image_H_28.284_a4674159.png' \n",
+      "H = 33.636 -> output_filename='2024-07-14_caustique/caustique_square-image_H_33.636_d9a7af9e.png' \n",
+      "H = 40.000 -> output_filename='2024-07-14_caustique/caustique_square-image_H_40.000_a1234263.png' \n"
+     ]
+    }
+   ],
    "source": [
     "for H_ in c.opt.H*np.logspace(-1, 1, N_scan, base=base):\n",
     "    opt = init()\n",
@@ -1101,7 +1573,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 39,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
@@ -1110,7 +1582,75 @@
      "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
     }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "radius=0.111 -> output_filename='2024-07-14_caustique/caustique_square-image_radius=0.111_00468503.png' \n",
+      "radius=0.222 -> output_filename='2024-07-14_caustique/caustique_square-image_radius=0.222_39ff64df.png' \n",
+      "radius=0.333 -> output_filename='2024-07-14_caustique/caustique_square-image_radius=0.333_8b81f3d3.png' \n",
+      "radius=0.444 -> output_filename='2024-07-14_caustique/caustique_square-image_radius=0.444_931bdf60.png' \n",
+      "radius=0.556 -> output_filename='2024-07-14_caustique/caustique_square-image_radius=0.556_e7c4815c.png' \n",
+      "radius=0.667 -> output_filename='2024-07-14_caustique/caustique_square-image_radius=0.667_aad700a5.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [02:58<00:00,  2.21s/it]\n",
+      "100%|██████████| 1/1 [02:58<00:00, 178.96s/it]\n",
+      "100%|██████████| 1/1 [00:07<00:00,  7.65s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "radius=0.778 -> output_filename='2024-07-14_caustique/caustique_square-image_radius=0.778_d61a88b5.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [02:54<00:00,  2.15s/it]\n",
+      "100%|██████████| 1/1 [02:54<00:00, 174.05s/it]\n",
+      "100%|██████████| 1/1 [00:09<00:00,  9.96s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "radius=0.889 -> output_filename='2024-07-14_caustique/caustique_square-image_radius=0.889_d328da03.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [02:54<00:00,  2.15s/it]\n",
+      "100%|██████████| 1/1 [02:54<00:00, 174.55s/it]\n",
+      "100%|██████████| 1/1 [00:12<00:00, 12.24s/it]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "radius=1.000 -> output_filename='2024-07-14_caustique/caustique_square-image_radius=1.000_e8508b3d.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n"
+     ]
+    }
+   ],
    "source": [
     "for radius in np.linspace(0, 1, N_scan+1)[1:]:\n",
     "    opt = init()\n",
@@ -1134,7 +1674,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 40,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1143,9 +1683,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 41,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "def generate_image(nx, ny, radius_in=0., radius_out=.9):\n",
     "    X, Y = np.meshgrid(np.linspace(-1, 1, nx, endpoint=True), np.linspace(-1, 1, ny, endpoint=True))\n",
@@ -1157,9 +1708,31 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 42,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [02:54<00:00,  2.16s/it]\n",
+      "100%|██████████| 1/1 [02:54<00:00, 174.96s/it]\n",
+      "100%|██████████| 1/1 [00:07<00:00,  7.88s/it]\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<img src=\"2024-07-14_caustique/caustique_disk-image_b7bfbb25.png\" width=\"1024\"/>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Image object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
    "source": [
     "c = Caustique(init())\n",
     "c.opt.tag = f'{c.opt.tag}_{type}-image'\n",
@@ -1169,7 +1742,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 43,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
@@ -1178,7 +1751,135 @@
      "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
     }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "H = 10.000 -> output_filename='2024-07-14_caustique/caustique_disk-image_H_10.000_e9ee9daa.png' \n",
+      "H = 11.892 -> output_filename='2024-07-14_caustique/caustique_disk-image_H_11.892_7f157ba1.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [02:48<00:00,  2.08s/it]\n",
+      "100%|██████████| 1/1 [02:48<00:00, 168.36s/it]\n",
+      "100%|██████████| 1/1 [00:07<00:00,  7.12s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "H = 14.142 -> output_filename='2024-07-14_caustique/caustique_disk-image_H_14.142_6b8bc48c.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [02:49<00:00,  2.10s/it]\n",
+      "100%|██████████| 1/1 [02:49<00:00, 169.93s/it]\n",
+      "100%|██████████| 1/1 [00:07<00:00,  7.26s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "H = 16.818 -> output_filename='2024-07-14_caustique/caustique_disk-image_H_16.818_68d5f977.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [02:52<00:00,  2.13s/it]\n",
+      "100%|██████████| 1/1 [02:52<00:00, 172.69s/it]\n",
+      "100%|██████████| 1/1 [00:07<00:00,  7.89s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "H = 20.000 -> output_filename='2024-07-14_caustique/caustique_disk-image_H_20.000_8c8148a7.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [02:53<00:00,  2.14s/it]\n",
+      "100%|██████████| 1/1 [02:53<00:00, 173.07s/it]\n",
+      "100%|██████████| 1/1 [00:08<00:00,  8.08s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "H = 23.784 -> output_filename='2024-07-14_caustique/caustique_disk-image_H_23.784_a8b0ecba.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [02:56<00:00,  2.18s/it]\n",
+      "100%|██████████| 1/1 [02:56<00:00, 176.30s/it]\n",
+      "100%|██████████| 1/1 [00:08<00:00,  8.02s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "H = 28.284 -> output_filename='2024-07-14_caustique/caustique_disk-image_H_28.284_82d58723.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [03:02<00:00,  2.25s/it]\n",
+      "100%|██████████| 1/1 [03:02<00:00, 182.49s/it]\n",
+      "100%|██████████| 1/1 [00:09<00:00,  9.44s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "H = 33.636 -> output_filename='2024-07-14_caustique/caustique_disk-image_H_33.636_a39ed8eb.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [03:02<00:00,  2.26s/it]\n",
+      "100%|██████████| 1/1 [03:02<00:00, 182.86s/it]\n",
+      "100%|██████████| 1/1 [00:08<00:00,  8.88s/it]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "H = 40.000 -> output_filename='2024-07-14_caustique/caustique_disk-image_H_40.000_5cd93cdb.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n"
+     ]
+    }
+   ],
    "source": [
     "for H_ in c.opt.H*np.logspace(-1, 1, N_scan, base=base):\n",
     "    opt = init()\n",
@@ -1193,7 +1894,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 44,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
@@ -1202,7 +1903,159 @@
      "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
     }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [02:54<00:00,  2.15s/it]\n",
+      "100%|██████████| 1/1 [02:54<00:00, 174.39s/it]\n",
+      "100%|██████████| 1/1 [00:02<00:00,  2.12s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.111 -> output_filename='2024-07-14_caustique/caustique_disk-image_radius_out=0.111_f3fc86c5.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [02:53<00:00,  2.15s/it]\n",
+      "100%|██████████| 1/1 [02:53<00:00, 173.75s/it]\n",
+      "100%|██████████| 1/1 [00:02<00:00,  2.12s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.222 -> output_filename='2024-07-14_caustique/caustique_disk-image_radius_out=0.222_3a288309.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [02:55<00:00,  2.16s/it]\n",
+      "100%|██████████| 1/1 [02:55<00:00, 175.33s/it]\n",
+      "100%|██████████| 1/1 [00:02<00:00,  2.56s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.333 -> output_filename='2024-07-14_caustique/caustique_disk-image_radius_out=0.333_9ffb2eba.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [02:37<00:00,  1.95s/it]\n",
+      "100%|██████████| 1/1 [02:37<00:00, 157.58s/it]\n",
+      "100%|██████████| 1/1 [00:02<00:00,  2.86s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.444 -> output_filename='2024-07-14_caustique/caustique_disk-image_radius_out=0.444_577b8bbc.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [02:32<00:00,  1.88s/it]\n",
+      "100%|██████████| 1/1 [02:32<00:00, 152.35s/it]\n",
+      "100%|██████████| 1/1 [00:03<00:00,  3.40s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.556 -> output_filename='2024-07-14_caustique/caustique_disk-image_radius_out=0.556_e0573034.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [02:26<00:00,  1.80s/it]\n",
+      "100%|██████████| 1/1 [02:26<00:00, 146.14s/it]\n",
+      "100%|██████████| 1/1 [00:04<00:00,  4.32s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.667 -> output_filename='2024-07-14_caustique/caustique_disk-image_radius_out=0.667_ea0f63d0.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [02:26<00:00,  1.80s/it]\n",
+      "100%|██████████| 1/1 [02:26<00:00, 146.10s/it]\n",
+      "100%|██████████| 1/1 [00:05<00:00,  5.46s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.778 -> output_filename='2024-07-14_caustique/caustique_disk-image_radius_out=0.778_d52eb8d7.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [02:26<00:00,  1.81s/it]\n",
+      "100%|██████████| 1/1 [02:26<00:00, 146.24s/it]\n",
+      "100%|██████████| 1/1 [00:07<00:00,  7.07s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.889 -> output_filename='2024-07-14_caustique/caustique_disk-image_radius_out=0.889_3d0086d5.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [02:25<00:00,  1.80s/it]\n",
+      "100%|██████████| 1/1 [02:25<00:00, 145.78s/it]\n",
+      "100%|██████████| 1/1 [00:08<00:00,  8.63s/it]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1.000 -> output_filename='2024-07-14_caustique/caustique_disk-image_radius_out=1.000_5b486f33.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n"
+     ]
+    }
+   ],
    "source": [
     "for radius_out in np.linspace(0, 1, N_scan+1)[1:]:\n",
     "    opt = init()\n",
@@ -1217,7 +2070,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 45,
    "metadata": {
     "execution": {
      "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
@@ -1226,7 +2079,19 @@
      "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
     }
    },
-   "outputs": [],
+   "outputs": [
+    {
+     "ename": "NameError",
+     "evalue": "name 'radius_in' is not defined",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
+      "Cell \u001b[0;32mIn[45], line 5\u001b[0m\n\u001b[1;32m      2\u001b[0m opt \u001b[38;5;241m=\u001b[39m init()\n\u001b[1;32m      3\u001b[0m c \u001b[38;5;241m=\u001b[39m Caustique(opt)\n\u001b[0;32m----> 5\u001b[0m c\u001b[38;5;241m.\u001b[39mopt\u001b[38;5;241m.\u001b[39mtag \u001b[38;5;241m=\u001b[39m \u001b[38;5;124mf\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;132;01m{\u001b[39;00mc\u001b[38;5;241m.\u001b[39mopt\u001b[38;5;241m.\u001b[39mtag\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m_\u001b[39m\u001b[38;5;132;01m{\u001b[39;00m\u001b[38;5;28mtype\u001b[39m\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m-image_\u001b[39m\u001b[38;5;132;01m{\u001b[39;00m\u001b[43mradius_in\u001b[49m\u001b[38;5;132;01m=:\u001b[39;00m\u001b[38;5;124m.3f\u001b[39m\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m'\u001b[39m\n\u001b[1;32m      6\u001b[0m image \u001b[38;5;241m=\u001b[39m generate_image(nx\u001b[38;5;241m=\u001b[39mc\u001b[38;5;241m.\u001b[39mopt\u001b[38;5;241m.\u001b[39mnx, ny\u001b[38;5;241m=\u001b[39mc\u001b[38;5;241m.\u001b[39mopt\u001b[38;5;241m.\u001b[39mny, radius_in\u001b[38;5;241m=\u001b[39mradius_in)\n\u001b[1;32m      7\u001b[0m output_filename \u001b[38;5;241m=\u001b[39m c\u001b[38;5;241m.\u001b[39mplot(z, image)\n",
+      "\u001b[0;31mNameError\u001b[0m: name 'radius_in' is not defined"
+     ]
+    }
+   ],
    "source": [
     "for radius in np.linspace(0, 1, N_scan+1)[1:]:\n",
     "    opt = init()\n",
@@ -1414,7 +2279,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.12.4"
+   "version": "3.10.12"
   },
   "nteract": {
    "version": "0.28.0"
diff --git a/2024-07-15_caustique-Granet.ipynb b/2024-07-15_caustique-Granet.ipynb
new file mode 100644
index 0000000..3aa4276
--- /dev/null
+++ b/2024-07-15_caustique-Granet.ipynb
@@ -0,0 +1,2414 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Caustics"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:17.668239Z",
+     "iopub.status.busy": "2022-09-16T06:50:17.667940Z",
+     "iopub.status.idle": "2022-09-16T06:50:17.670759Z",
+     "shell.execute_reply": "2022-09-16T06:50:17.670294Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "import os\n",
+    "import numpy as np\n",
+    "\n",
+    "# the higher PRECISION, the bigger the file\n",
+    "# PRECISION = 4  # debugging\n",
+    "# PRECISION = 10 # good quality\n",
+    "PRECISION = 12 # for production\n",
+    "# PRECISION = 13 # for production\n",
+    "\n",
+    "# https://docs.python.org/3/library/dataclasses.html?highlight=dataclass#module-dataclasses\n",
+    "from dataclasses import dataclass\n",
+    "\n",
+    "@dataclass\n",
+    "class init:\n",
+    "    figpath: str = '2024-07-15_caustique-Granet' # Folder to store images\n",
+    "    phi: float = 1.61803 # beauty is gold\n",
+    "    tag: str = 'caustique' # Tag\n",
+    "    ext: str = 'png' # Extension for output\n",
+    "    nx: int = 5*2**PRECISION # number of pixels (vertical)\n",
+    "    ny: int = 5*2**PRECISION # number of pixels (horizontal)\n",
+    "    nframe: int = 1 # number of frames\n",
+    "    bin_dens: int = 1 # relative bin density\n",
+    "    bin_spectrum: int = 1 # bin spacing in spectrum (lower is more CPU)\n",
+    "    seed: int = 2024 # seed for RNG\n",
+    "    H: float = 20.0 # depth of the pool\n",
+    "    variation: float = .20 # variation of diffraction index: http://www.philiplaven.com/p20.html 1.40 at 400 nm and 1.37 at 700nm makes a 2% variation\n",
+    "    scale: float = .50*2**PRECISION # period in pixels\n",
+    "    B_sf: float = 0.75 # bandwidth in sf\n",
+    "    V_Y: float = 0.3 # horizontal speed\n",
+    "    V_X: float = 0.3 # vertical speed\n",
+    "    B_V: float = 1.0 # bandwidth in speed\n",
+    "    zmin: float = 0.2 # gradient of wave height\n",
+    "    # theta: float = 2*np.pi*(2-1.61803) # angle with the horizontal\n",
+    "    theta: float = np.pi/2 # angle with the horizontal\n",
+    "    B_theta: float = 60*np.pi/180 # bandwidth in theta\n",
+    "    min_lum: float = .1 # diffusion level for the rendering\n",
+    "    gamma: float = 2.9 # Gamma exponant to convert luminosity to luminance\n",
+    "    fps: float = 18 # frames per second\n",
+    "    multispectral: bool = True # Compute caustics on the full spectrogram.\n",
+    "    cache: bool = False # Cache intermediate output.\n",
+    "    verbose: bool = True # Displays more verbose output.\n",
+    "    do_display: bool = True # Displays images in notebook.\n",
+    "    do_recompute: bool = True # Restart each computation    "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:17.688713Z",
+     "iopub.status.busy": "2022-09-16T06:50:17.688504Z",
+     "iopub.status.idle": "2022-09-16T06:50:17.691583Z",
+     "shell.execute_reply": "2022-09-16T06:50:17.691125Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Saving our simulations in=2024-07-15_caustique-Granet\n"
+     ]
+    }
+   ],
+   "source": [
+    "opt = init()\n",
+    "print(f'Saving our simulations in={opt.figpath}')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "if opt.nframe==1: opt.ext = 'png'"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:17.728359Z",
+     "iopub.status.busy": "2022-09-16T06:50:17.728155Z",
+     "iopub.status.idle": "2022-09-16T06:50:17.734829Z",
+     "shell.execute_reply": "2022-09-16T06:50:17.734354Z"
+    },
+    "tags": []
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "init(figpath='2024-07-15_caustique-Granet',\n",
+      "     phi=1.61803,\n",
+      "     tag='caustique',\n",
+      "     ext='tiff',\n",
+      "     nx=20480,\n",
+      "     ny=20480,\n",
+      "     nframe=1,\n",
+      "     bin_dens=1,\n",
+      "     bin_spectrum=1,\n",
+      "     seed=2024,\n",
+      "     H=20.0,\n",
+      "     variation=0.2,\n",
+      "     scale=2048.0,\n",
+      "     B_sf=0.75,\n",
+      "     V_Y=0.3,\n",
+      "     V_X=0.3,\n",
+      "     B_V=1.0,\n",
+      "     zmin=0.2,\n",
+      "     theta=1.5707963267948966,\n",
+      "     B_theta=1.0471975511965976,\n",
+      "     min_lum=0.1,\n",
+      "     gamma=2.9,\n",
+      "     fps=18,\n",
+      "     multispectral=True,\n",
+      "     cache=False,\n",
+      "     verbose=True,\n",
+      "     do_display=True,\n",
+      "     do_recompute=True)\n"
+     ]
+    }
+   ],
+   "source": [
+    "from pprint import pprint\n",
+    "pprint(opt)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## utilities\n",
+    "\n",
+    "Transfoming a sequence of PNG frames into gif or mp4:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:17.737334Z",
+     "iopub.status.busy": "2022-09-16T06:50:17.737126Z",
+     "iopub.status.idle": "2022-09-16T06:50:17.741165Z",
+     "shell.execute_reply": "2022-09-16T06:50:17.740716Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "def make_gif(gifname, fnames, fps, do_delete=True):\n",
+    "    import imageio\n",
+    "\n",
+    "    with imageio.get_writer(gifname, mode='I', fps=fps) as writer:\n",
+    "        for fname in fnames:\n",
+    "            writer.append_data(imageio.imread(fname))\n",
+    "\n",
+    "    from pygifsicle import optimize\n",
+    "    optimize(str(gifname))\n",
+    "    if do_delete: \n",
+    "        for fname in fnames: os.remove(fname)\n",
+    "    return gifname\n",
+    "\n",
+    "# https://moviepy.readthedocs.io/en/latest/getting_started/videoclips.html#imagesequenceclip\n",
+    "def make_mp4(mp4name, fnames, fps, do_delete=True):\n",
+    "    import moviepy.editor as mpy\n",
+    "    clip = mpy.ImageSequenceClip(fnames, fps=fps)\n",
+    "    clip.write_videofile(mp4name, fps=fps, codec='libx264', verbose=False, logger=None)\n",
+    "    if do_delete: \n",
+    "        for fname in fnames: os.remove(fname)\n",
+    "    return mp4name"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "\n",
+    "Utilities to compute the spectrum of the blue sky and convert them later to RGB values (check out https://laurentperrinet.github.io/sciblog/posts/2020-07-04-colors-of-the-sky.html for details)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:17.743669Z",
+     "iopub.status.busy": "2022-09-16T06:50:17.743461Z",
+     "iopub.status.idle": "2022-09-16T06:50:17.757701Z",
+     "shell.execute_reply": "2022-09-16T06:50:17.757282Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "from lambda2color import Lambda2color, xyz_from_xy\n",
+    "\n",
+    "# borrowed from https://github.com/gummiks/gummiks.github.io/blob/master/scripts/astro/planck.py\n",
+    "def planck(wav, T):\n",
+    "    import scipy.constants as const\n",
+    "    c = const.c # c = 3.0e+8\n",
+    "    h = const.h # h = 6.626e-34\n",
+    "    k = const.k # k = 1.38e-23\n",
+    "    a = 2.0*h*c**2\n",
+    "    b = h*c/(wav*k*T)\n",
+    "    intensity = a / ( (wav**5) * (np.exp(b) - 1.0) )\n",
+    "    return intensity\n",
+    "\n",
+    "def scattering(wav, a=0.005, p=1.3, b=0.45):\n",
+    "    \"\"\"\n",
+    "    b is  proportionate  to  the  column  density  of  aerosols\n",
+    "    along  the  path  of  sunlight,  from  outside  the  atmosphere\n",
+    "    to  the  point  of  observation\n",
+    "    \n",
+    "    see https://laurentperrinet.github.io/sciblog/posts/2020-07-04-colors-of-the-sky.html for more details\n",
+    "\n",
+    "    \"\"\"\n",
+    "    # converting wav in µm:\n",
+    "    intensity = np.exp(-a/((wav/1e-6)**4)) # Rayleigh extinction by nitrogen\n",
+    "    intensity *= (wav/1e-6)**-4\n",
+    "    intensity *= np.exp(-b/((wav/1e-6)**p)) # Aerosols\n",
+    "    return intensity"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## computing the caustics"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:17.012647Z",
+     "iopub.status.busy": "2022-09-16T06:50:17.012413Z",
+     "iopub.status.idle": "2022-09-16T06:50:17.665184Z",
+     "shell.execute_reply": "2022-09-16T06:50:17.664652Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "import matplotlib\n",
+    "import matplotlib.pyplot as plt\n",
+    "from tqdm import tqdm, trange\n",
+    "import shutil\n",
+    "import hashlib\n",
+    "import MotionClouds as mc\n",
+    "\n",
+    "class Caustique:\n",
+    "    def __init__(self, opt):\n",
+    "        \"\"\"\n",
+    "        Image coordinates follow 'ij' indexing, that is,\n",
+    "        * their origin at the top left,\n",
+    "        * the X axis is vertical and goes \"down\",\n",
+    "        * the Y axis is horizontal and goes \"right\".\n",
+    "\n",
+    "        \"\"\"\n",
+    "        self.mc = mc\n",
+    "        self.ratio = opt.ny/opt.nx # ratio between height and width (>1 for portrait, <1 for landscape)\n",
+    "        X = np.linspace(0, 1, opt.nx, endpoint=False) # vertical\n",
+    "        Y = np.linspace(0, self.ratio, opt.ny, endpoint=False) # horizontal\n",
+    "        self.xv, self.yv = np.meshgrid(X, Y, indexing='ij')\n",
+    "        self.opt = opt\n",
+    "        # https://stackoverflow.com/questions/16878315/what-is-the-right-way-to-treat-python-argparse-namespace-as-a-dictionary\n",
+    "        self.d = vars(opt)\n",
+    "        os.makedirs(self.opt.figpath, exist_ok=True)\n",
+    "        self.cachepath = os.path.join('/tmp', self.opt.figpath)\n",
+    "        if opt.verbose: print(f'{self.cachepath=}')\n",
+    "        os.makedirs(self.cachepath, exist_ok=True)\n",
+    "\n",
+    "        # a standard white:\n",
+    "        # illuminant_D65 = xyz_from_xy(0.3127, 0.3291), \n",
+    "        illuminant_sun = xyz_from_xy(0.325998, 0.335354)\n",
+    "        # color conversion class\n",
+    "        self.cs_srgb = Lambda2color(red=xyz_from_xy(0.64, 0.33),\n",
+    "                               green=xyz_from_xy(0.30, 0.60),\n",
+    "                               blue=xyz_from_xy(0.15, 0.06),\n",
+    "                               white=illuminant_sun)\n",
+    "        self.wavelengths = self.cs_srgb.cmf[:, 0]*1e-9\n",
+    "        self.N_wavelengths = len(self.wavelengths)\n",
+    "        # multiply by the spectrum of the sky\n",
+    "        intensity5800 = planck(self.wavelengths, 5800.)\n",
+    "        scatter = scattering(self.wavelengths)\n",
+    "        self.spectrum_sky = intensity5800 * scatter\n",
+    "        self.spectrum_sky /= self.spectrum_sky.max()\n",
+    "\n",
+    "    def wave(self):\n",
+    "        filename = f'{self.cachepath}/{self.opt.tag}_wave.npy'\n",
+    "        if os.path.isfile(filename) and not(self.opt.do_recompute):\n",
+    "            z = np.load(filename)\n",
+    "        else:\n",
+    "            # A simplistic model of a wave using https://github.com/NeuralEnsemble/MotionClouds\n",
+    "            fx, fy, ft = mc.get_grids(self.opt.nx, self.opt.ny, self.opt.nframe)\n",
+    "            env = mc.envelope_gabor(fx, fy, ft, V_X=self.opt.V_Y, V_Y=self.opt.V_X, B_V=self.opt.B_V,\n",
+    "                                    sf_0=1./self.opt.scale, B_sf=self.opt.B_sf/self.opt.scale,\n",
+    "                                    theta=self.opt.theta, B_theta=self.opt.B_theta)\n",
+    "            z = mc.rectif(mc.random_cloud(env, seed=self.opt.seed))\n",
+    "            if self.opt.cache: np.save(filename, z)\n",
+    "        return z * np.linspace(self.opt.zmin, 1., self.opt.nx)[:, None, None]\n",
+    "\n",
+    "    def transform(self, z_, modulation=1.):\n",
+    "        xv, yv = self.xv.copy(), self.yv.copy()\n",
+    "\n",
+    "        dzdx = z_ - np.roll(z_, 1, axis=0)\n",
+    "        dzdy = z_ - np.roll(z_, 1, axis=1)\n",
+    "        xv = xv + modulation * self.opt.H * dzdx\n",
+    "        yv = yv + modulation * self.opt.H * dzdy\n",
+    "\n",
+    "        xv = np.mod(xv, 1)\n",
+    "        yv = np.mod(yv, self.ratio)\n",
+    "\n",
+    "        return xv, yv\n",
+    "\n",
+    "    def plot(self, z, image=None, do_color=True, dpi=50):\n",
+    "        \"\"\"\n",
+    "        \n",
+    "        dpi: output resolution - sets the figure size as we ensure there is a one to one correspondance between pixels in the data and the output image\n",
+    "        \"\"\"\n",
+    "\n",
+    "        # output filename        \n",
+    "        md5 = hashlib.sha224((self.opt.figpath + self.opt.tag).encode()).hexdigest()[:8] # an unique identifier for future tagging\n",
+    "        output_filename = f'{self.opt.figpath}/{self.opt.tag}_{md5}.{self.opt.ext}'\n",
+    "        if os.path.isfile(output_filename) and not(self.opt.do_recompute):\n",
+    "            return output_filename\n",
+    "        else:\n",
+    "            # 1/ do the raytracing of image through z:\n",
+    "            binsx, binsy = self.opt.nx//self.opt.bin_dens, self.opt.ny//self.opt.bin_dens\n",
+    "\n",
+    "            # a fixed image in degree of contrast (from 0=black to 1=white)\n",
+    "            if image is None: image = np.ones((self.opt.nx, self.opt.ny))\n",
+    "\n",
+    "            #hist = self.do_raytracing(z)\n",
+    "            # binsx, binsy = self.opt.nx//self.opt.bin_dens, self.opt.ny//self.opt.bin_dens\n",
+    "\n",
+    "            subplotpars = matplotlib.figure.SubplotParams(left=0., right=1., bottom=0., top=1., wspace=0., hspace=0.,)\n",
+    "\n",
+    "            if self.opt.multispectral:\n",
+    "\n",
+    "                #image_rgb = self.cs_srgb.spec_to_rgb(hist)\n",
+    "                image_rgb = np.zeros((self.opt.nx//self.opt.bin_dens,  self.opt.ny//self.opt.bin_dens, 3, self.opt.nframe))\n",
+    "                for i_frame in trange(self.opt.nframe):\n",
+    "                    for i_wavelength in trange(self.opt.bin_spectrum//2, self.N_wavelengths, self.opt.bin_spectrum):\n",
+    "                        modulation = 1. + self.opt.variation/2 - self.opt.variation*i_wavelength/self.N_wavelengths\n",
+    "                        xv, yv = self.transform(z[:, :, i_frame], modulation=modulation)\n",
+    "                        hist_, _, _ = np.histogram2d(xv.ravel(), yv.ravel(),\n",
+    "                                                     bins=[binsx, binsy],\n",
+    "                                                     weights=image.ravel(),\n",
+    "                                                     range=[[0, 1], [0, self.ratio]],\n",
+    "                                                     density=True)\n",
+    "\n",
+    "                        # we convert the spectrum into a color\n",
+    "                        spec = np.zeros((self.N_wavelengths))\n",
+    "                        spec[i_wavelength] = 1\n",
+    "                        rgb = self.cs_srgb.spec_to_rgb(spec)\n",
+    "                        rgb *= self.spectrum_sky[i_wavelength]\n",
+    "                        # we add the color to the image\n",
+    "                        image_rgb[:, :, :, i_frame] += hist_[:, :, None] * rgb[None, None, :]\n",
+    "\n",
+    "                image_rgb -= image_rgb.min()\n",
+    "                image_rgb /= image_rgb.max()\n",
+    "            else:\n",
+    "                hist = np.zeros((binsx, binsy, self.opt.nframe))\n",
+    "                for i_frame in trange(self.opt.nframe):\n",
+    "                    xv, yv = self.transform(z[:, :, i_frame])\n",
+    "                    hist_, _, _ = np.histogram2d(xv.ravel(), yv.ravel(),\n",
+    "                                                        bins=[binsx, binsy],\n",
+    "                                                        range=[[0, 1], [0, self.ratio]],\n",
+    "                                                        density=True)\n",
+    "                #hist /= hist.max()\n",
+    "\n",
+    "            # 2/ transform light into image:\n",
+    "            fnames = []\n",
+    "            for i_frame in trange(self.opt.nframe):\n",
+    "                fig, ax = plt.subplots(figsize=(self.opt.ny/self.opt.bin_dens/dpi, self.opt.nx/self.opt.bin_dens/dpi), subplotpars=subplotpars)\n",
+    "                if self.opt.multispectral:\n",
+    "                    ax.imshow(image_rgb[:, :, :, i_frame] ** (1/self.opt.gamma), vmin=0, vmax=1)\n",
+    "                else:\n",
+    "                    if do_color:\n",
+    "                        bluesky = np.array([0.268375, 0.283377]) # xyz\n",
+    "                        sun = np.array([0.325998, 0.335354]) # xyz\n",
+    "                        # ax.pcolormesh(edge_y, edge_x, hist[:, :, i_frame], vmin=0, vmax=1, cmap=plt.cm.Blues_r)\n",
+    "                        # https://en.wikipedia.org/wiki/CIE_1931_color_space#Mixing_colors_specified_with_the_CIE_xy_chromaticity_diagram\n",
+    "                        L1 = 1 - hist[:, :, i_frame]\n",
+    "                        L2 = hist[:, :, i_frame]\n",
+    "                        image_denom = L1 / bluesky[1] + L2 / sun[1]\n",
+    "                        image_x = (L1 * bluesky[0] / bluesky[1] + L2 * sun[0] / sun[1]) / image_denom\n",
+    "                        image_y = (L1 + L2) / image_denom \n",
+    "                        image_xyz = np.dstack((image_x, image_y, 1 - image_x - image_y))\n",
+    "                        image_rgb = self.cs_srgb.xyz_to_rgb(image_xyz)\n",
+    "                        image_L = self.opt.min_lum + (1-self.opt.min_lum)* L2 ** .61803\n",
+    "                        ax.imshow(image_L[:, :, None]*image_rgb, vmin=0, vmax=1)\n",
+    "\n",
+    "                    else:\n",
+    "                        ax.imshow(1-image_L, vmin=0, vmax=1)\n",
+    "\n",
+    "                fname = f'{self.cachepath}/{self.opt.tag}_frame_{i_frame:04d}.png'\n",
+    "                fig.savefig(fname, dpi=dpi)\n",
+    "                fnames.append(fname)\n",
+    "                plt.close('all')\n",
+    "\n",
+    "            if self.opt.nframe==1:\n",
+    "                shutil.copyfile(fname, output_filename)\n",
+    "                return output_filename\n",
+    "            else:\n",
+    "                if self.opt.ext == 'gif':\n",
+    "                    return make_gif(output_filename, fnames, fps=self.opt.fps)\n",
+    "                else:\n",
+    "                    return make_mp4(output_filename, fnames, fps=self.opt.fps)\n",
+    "\n",
+    "    def show(self, output_filename, width=1024):\n",
+    "        from IPython.display import HTML, Image, display\n",
+    "        if self.opt.nframe==1:\n",
+    "            display(Image(url=output_filename.replace(self.opt.ext, 'png'), width=width))\n",
+    "        else:\n",
+    "            if self.opt.ext == 'gif':\n",
+    "                return display(Image(url=output_filename, width=width))\n",
+    "            else:\n",
+    "                #import moviepy.editor as mpy\n",
+    "                #return mpy.ipython_display(output_filename, width=width)\n",
+    "                # https://github.com/NeuralEnsemble/MotionClouds/blob/master/MotionClouds/MotionClouds.py#L858\n",
+    "                opts = ' loop=\"1\" autoplay=\"1\" controls '\n",
+    "                html = HTML(f'<video {opts} width=\"{width}\"> <source src=\"{output_filename}\" type=\"video/{self.opt.ext}\" />  </video>')\n",
+    "                html.reload()\n",
+    "                return display(html)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# the selected caustics"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:17.864888Z",
+     "iopub.status.busy": "2022-09-16T06:50:17.864663Z",
+     "iopub.status.idle": "2022-09-16T06:50:19.896847Z",
+     "shell.execute_reply": "2022-09-16T06:50:19.896285Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "self.cachepath='/tmp/2024-07-15_caustique-Granet'\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "(20480, 20480, 1)"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "c = Caustique(opt)\n",
+    "z = c.wave()\n",
+    "z.shape"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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33ilffPGFjBkzJpzLkcLCQlm2bJn1OBgMSmZmZljnBABcncIWkMeOHZMPP/zQemd4Kbm5uSIicuTIERkzZox4PB755JNPbDXNzc0iIuLxeKx/dh+7sMbtdl/y3aOIiMvlEpfLFfJeAADRJ2zfg1y/fr2kpqZKfn7+ZetqampERCQ9PV1ERLxerxw8eFBaWlqsmpKSEnG73XLjjTdaNaWlpbbrlJSUiNfr7cUdAACiWjju/Dl//rwOHz5cV6xYYTt+5MgRff7553Xfvn3a0NCg7777ro4ePVqnTZtm1XR2duqECRN0+vTpWlNTozt27NChQ4dqYWGhVfPll19qQkKCFhQUaF1dnRYXF+uAAQN0x44dIa2Tu1j757z0mL32173S477pcagjXHexhiUgP/jgAxURra+vtx1vbGzUadOm6eDBg9XlcunYsWO1oKDgos0dPXpUZ86cqfHx8ZqSkqLLly/Xjo4OW01ZWZlOmjRJnU6njh49WtevXx/yOgnI/jkvPWav/XWv9LhvehzqCFdAOv6+uagUDAYlMTExomvoafsv/JhMX80ZqXl7c85IzRtNPY6mvUZq3mjrcagCgYC43e5evy4/ixUAAAMCEgAAAwISAAADAhIAAAMCEgAAAwISAAADAhIAAAMCEgAAAwISAAADAhIAAAMCEgAAAwISAAADAhIAAAMCEgAAAwISAAADAhIAAAMCEgAAAwISAAADAhIAAAMCEgAAAwISAAADAhIAAAMCEgAAAwISAAADAhIAAAMCEgAAAwISAAADAhIAAAMCEgAAAwISAAADAhIAAAMCEgAAAwISAAADAhIAAIOQA7KiokLuuusuycjIEIfDIVu3brWdV1V55plnJD09XeLj4yUvL08+//xzW83Jkydl3rx54na7JSkpSRYsWCCnTp2y1Rw4cECmTp0qcXFxkpmZKatXr75oLZs3b5bx48dLXFyc5OTkyPbt20PdDgAARiEH5LfffisTJ06U4uJi4/nVq1fLf/7nf8p//dd/yd69e+UHP/iB+Hw+OXv2rFUzb948OXTokJSUlMh7770nFRUV8sgjj1jng8GgTJ8+XUaMGCFVVVWyZs0aefbZZ+W1116zavbs2SNz586VBQsWSHV1tcyaNUtmzZoltbW1oW4JAICL6RUQEd2yZYv1uKurSz0ej65Zs8Y61traqi6XS99++21VVT18+LCKiH766adWzfvvv68Oh0O/+uorVVV99dVXNTk5Wdvb262aFStWaFZWlvV49uzZmp+fb1tPbm6uLlq0qMfrDwQCKiIRHT0ViTkjNS89Zq/9da/0uG96HOoIBAIh9ainevV7kA0NDeL3+yUvL886lpiYKLm5uVJZWSkiIpWVlZKUlCS33HKLVZOXlycxMTGyd+9eq2batGnidDqtGp/PJ/X19fLNN99YNRfO013TPY9Je3u7BINB2wAAwKRXA9Lv94uISFpamu14Wlqadc7v90tqaqrt/MCBA2Xw4MG2GtM1LpzjUjXd502KiookMTHRGpmZmaFuEQAQJaLqLtbCwkIJBALWOH78eKSXBADop3o1ID0ej4iINDc32443Nzdb5zwej7S0tNjOd3Z2ysmTJ201pmtcOMelarrPm7hcLnG73bYBAIBJrwbkqFGjxOPxSGlpqXUsGAzK3r17xev1ioiI1+uV1tZWqaqqsmp27twpXV1dkpuba9VUVFRIR0eHVVNSUiJZWVmSnJxs1Vw4T3dN9zwAAFyRUO/qaWtr0+rqaq2urlYR0Zdeekmrq6v12LFjqqq6atUqTUpK0nfffVcPHDig99xzj44aNUrPnDljXWPGjBl688036969e/Wjjz7SG264QefOnWudb21t1bS0NL3//vu1trZWN27cqAkJCbpu3TqrZvfu3Tpw4EB98cUXta6uTleuXKmxsbF68ODBHu+Fu1j757z0mL32173S477pcagjXHexhhyQZWVlxgXOnz9fVf/2UY+nn35a09LS1OVy6Z133qn19fW2a5w4cULnzp2rgwYNUrfbrQ899JC2tbXZavbv36933HGHulwuHTZsmK5ateqitWzatEnHjRunTqdTs7Ozddu2bSHthYDsn/PSY/baX/dKj/umx6GOcAWk4++bi0rBYFASExMjuoaett/hcPT5nJGatzfnjNS80dTjaNprpOaNth6HKhAIhOWekqi6ixUAgJ4iIAEAMCAgAQAwICABADAgIAEAMCAgAQAwICABADAgIAEAMCAgAQAwICABADAgIAEAMCAgAQAwICABADAgIAEAMCAgAQAwICABADAgIAEAMCAgAQAwICABADAgIAEAMCAgAQAwICABADAgIAEAMCAgAQAwICABADAgIAEAMCAgAQAwICABADAgIAEAMCAgAQAwICABADAgIAEAMCAgAQAwICABADAgIAEAMAg5ICsqKuSuu+6SjIwMcTgcsnXrVutcR0eHrFixQnJycuQHP/iBZGRkyAMPPCB/+ctfbNcYOXKkOBwO21i1apWt5sCBAzJ16lSJi4uTzMxMWb169UVr2bx5s4wfP17i4uIkJydHtm/fHup2AAAwCjkgv/32W5k4caIUFxdfdO706dPy2WefydNPPy2fffaZvPPOO1JfXy933333RbXPP/+8NDU1WePxxx+3zgWDQZk+fbqMGDFCqqqqZM2aNfLss8/Ka6+9ZtXs2bNH5s6dKwsWLJDq6mqZNWuWzJo1S2pra0PdEgAAF9MrICK6ZcuWy9Z88sknKiJ67Ngx69iIESP05ZdfvuRzXn31VU1OTtb29nbr2IoVKzQrK8t6PHv2bM3Pz7c9Lzc3VxctWnTJ6549e1YDgYA1jh8/riIS0dFTkZgzUvPSY/baX/dKj/umx6GOQCAQUo96KuzfgwwEAuJwOCQpKcl2fNWqVTJkyBC5+eabZc2aNdLZ2Wmdq6yslGnTponT6bSO+Xw+qa+vl2+++caqycvLs13T5/NJZWXlJddSVFQkiYmJ1sjMzOyFHQIArkVhDcizZ8/KihUrZO7cueJ2u63jv/71r2Xjxo1SVlYmixYtkhdeeEGeeuop67zf75e0tDTbtbof+/3+y9Z0nzcpLCyUQCBgjePHj1/xHgEA16aB4bpwR0eHzJ49W1RV1q5dazu3bNky6+ubbrpJnE6nLFq0SIqKisTlcoVrSeJyucJ6fQDAtSMs7yC7w/HYsWNSUlJie/dokpubK52dnXL06FEREfF4PNLc3Gyr6X7s8XguW9N9HgCAK9HrAdkdjp9//rl8+OGHMmTIkO98Tk1NjcTExEhqaqqIiHi9XqmoqJCOjg6rpqSkRLKysiQ5OdmqKS0ttV2npKREvF5vL+4GABC1Qr2rp62tTaurq7W6ulpFRF966SWtrq7WY8eO6blz5/Tuu+/W66+/XmtqarSpqcka3Xek7tmzR19++WWtqanRL774Qt98800dOnSoPvDAA9Ycra2tmpaWpvfff7/W1tbqxo0bNSEhQdetW2fV7N69WwcOHKgvvvii1tXV6cqVKzU2NlYPHjzY470EAoGI333VU5GYM1Lz0mP22l/3So/7psehjnDdxRpyQJaVlRkXOH/+fG1oaLjkBsrKylRVtaqqSnNzczUxMVHj4uL0hz/8ob7wwgt69uxZ2zz79+/XO+64Q10ulw4bNkxXrVp10Vo2bdqk48aNU6fTqdnZ2bpt27aQ9kJA9s956TF77a97pcd90+NQR7gC0vH3zUWlYDAoiYmJEV1DT9vvcDj6fM5Izdubc0Zq3mjqcTTtNVLzRluPQxUIBL7zXpfvg5/FCgCAAQEJAIABAQkAgAEBCQCAAQEJAIABAQkAgAEBCQCAAQEJAIABAQkAgAEBCQCAAQEJAIABAQkAgAEBCQCAAQEJAIABAQkAgAEBCQCAAQEJAIABAQkAgAEBCQCAAQEJAIABAQkAgAEBCQCAAQEJAIABAQkAgAEBCQCAAQEJAIABAQkAgAEBCQCAAQEJAIABAQkAgAEBCQCAAQEJAIABAQkAgAEBCQCAQcgBWVFRIXfddZdkZGSIw+GQrVu32s4/+OCD4nA4bGPGjBm2mpMnT8q8efPE7XZLUlKSLFiwQE6dOmWrOXDggEydOlXi4uIkMzNTVq9efdFaNm/eLOPHj5e4uDjJycmR7du3h7odAACMQg7Ib7/9ViZOnCjFxcWXrJkxY4Y0NTVZ4+2337adnzdvnhw6dEhKSkrkvffek4qKCnnkkUes88FgUKZPny4jRoyQqqoqWbNmjTz77LPy2muvWTV79uyRuXPnyoIFC6S6ulpmzZols2bNktra2lC3BADAxfQKiIhu2bLFdmz+/Pl6zz33XPI5hw8fVhHRTz/91Dr2/vvvq8Ph0K+++kpVVV999VVNTk7W9vZ2q2bFihWalZVlPZ49e7bm5+fbrp2bm6uLFi265Nxnz57VQCBgjePHj6uIRHT0VCTmjNS89Ji99te90uO+6XGoIxAIhNSjngrL9yDLy8slNTVVsrKy5NFHH5UTJ05Y5yorKyUpKUluueUW61heXp7ExMTI3r17rZpp06aJ0+m0anw+n9TX18s333xj1eTl5dnm9fl8UllZecl1FRUVSWJiojUyMzN7Zb8AgGtPrwfkjBkz5A9/+IOUlpbKb3/7W9m1a5fMnDlTzp8/LyIifr9fUlNTbc8ZOHCgDB48WPx+v1WTlpZmq+l+/F013edNCgsLJRAIWOP48eNXtlkAwDVrYG9f8Je//KX1dU5Ojtx0000yZswYKS8vlzvvvLO3pwuJy+USl8sV0TUAAK4OYf+Yx+jRoyUlJUWOHDkiIiIej0daWlpsNZ2dnXLy5EnxeDxWTXNzs62m+/F31XSfBwDgSoQ9IP/85z/LiRMnJD09XUREvF6vtLa2SlVVlVWzc+dO6erqktzcXKumoqJCOjo6rJqSkhLJysqS5ORkq6a0tNQ2V0lJiXi93nBvCQAQDUK9q6etrU2rq6u1urpaRURfeuklra6u1mPHjmlbW5v+5je/0crKSm1oaNAPP/xQJ0+erDfccIOePXvWusaMGTP05ptv1r179+pHH32kN9xwg86dO9c639raqmlpaXr//fdrbW2tbty4URMSEnTdunVWze7du3XgwIH64osval1dna5cuVJjY2P14MGDPd5LIBCI+N1XPRWJOSM1Lz1mr/11r/S4b3oc6gjXXawhB2RZWZlxgfPnz9fTp0/r9OnTdejQoRobG6sjRozQhQsXqt/vt13jxIkTOnfuXB00aJC63W596KGHtK2tzVazf/9+veOOO9TlcumwYcN01apVF61l06ZNOm7cOHU6nZqdna3btm0LaS8EZP+clx6z1/66V3rcNz0OdYQrIB1/31xUCgaDkpiYGNE19LT9Doejz+eM1Ly9OWek5o2mHkfTXiM1b7T1OFSBQEDcbnevX5efxQoAgAEBCQCAAQEJAIABAQkAgAEBCQCAAQEJAIABAQkAgAEBCQCAAQEJAIABAQkAgAEBCQCAAQEJAIABAQkAgAEBCQCAAQEJAIABAQkAgAEBCQCAAQEJAIABAQkAgAEBCQCAAQEJAIABAQkAgAEBCQCAAQEJAIABAQkAgAEBCQCAAQEJAIABAQkAgAEBCQCAAQEJAIABAQkAgAEBCQCAAQEJAIABAQkAgEHIAVlRUSF33XWXZGRkiMPhkK1bt9rOOxwO41izZo1VM3LkyIvOr1q1ynadAwcOyNSpUyUuLk4yMzNl9erVF61l8+bNMn78eImLi5OcnBzZvn17qNsBAMAo5ID89ttvZeLEiVJcXGw839TUZBuvv/66OBwOue+++2x1zz//vK3u8ccft84Fg0GZPn26jBgxQqqqqmTNmjXy7LPPymuvvWbV7NmzR+bOnSsLFiyQ6upqmTVrlsyaNUtqa2tD3RIAABfTKyAiumXLlsvW3HPPPfoP//APtmMjRozQl19++ZLPefXVVzU5OVnb29utYytWrNCsrCzr8ezZszU/P9/2vNzcXF20aFGP1x8IBFREIjp6KhJzRmpeesxe++te6XHf9DjUEQgEQupRT4X1e5DNzc2ybds2WbBgwUXnVq1aJUOGDJGbb75Z1qxZI52dnda5yspKmTZtmjidTuuYz+eT+vp6+eabb6yavLw82zV9Pp9UVlZecj3t7e0SDAZtAwAAk4HhvPgbb7wh1113nfziF7+wHf/1r38tkydPlsGDB8uePXuksLBQmpqa5KWXXhIREb/fL6NGjbI9Jy0tzTqXnJwsfr/fOnZhjd/vv+R6ioqK5LnnnuuNrQEArnFhDcjXX39d5s2bJ3Fxcbbjy5Yts76+6aabxOl0yqJFi6SoqEhcLlfY1lNYWGibOxgMSmZmZtjmAwBcvcIWkH/605+kvr5e/vjHP35nbW5urnR2dsrRo0clKytLPB6PNDc322q6H3s8Huufppru8yYulyusAQwAuHaE7XuQv//972XKlCkyceLE76ytqamRmJgYSU1NFRERr9crFRUV0tHRYdWUlJRIVlaWJCcnWzWlpaW265SUlIjX6+3FXQAAolaod/W0tbVpdXW1VldXq4joSy+9pNXV1Xrs2DGrJhAIaEJCgq5du/ai5+/Zs0dffvllramp0S+++ELffPNNHTp0qD7wwANWTWtrq6alpen999+vtbW1unHjRk1ISNB169ZZNbt379aBAwfqiy++qHV1dbpy5UqNjY3VgwcP9ngv3MXaP+elx+y1v+6VHvdNj0Md4bqLNeSALCsrMy5w/vz5Vs26des0Pj5eW1tbL3p+VVWV5ubmamJiosbFxekPf/hDfeGFF/Ts2bO2uv379+sdd9yhLpdLhw0bpqtWrbroWps2bdJx48ap0+nU7Oxs3bZtW0h7ISD757z0mL32173S477pcagjXAHp+PvmolIwGJTExMSIrqGn7Xc4HH0+Z6Tm7c05IzVvNPU4mvYaqXmjrcehCgQC4na7e/26/CxWAAAMCEgAAAwISAAADAhIAAAMCEgAAAwISAAADAhIAAAMCEgAAAwISAAADAhIAAAMCEgAAAwISAAADAhIAAAMCEgAAAwISAAADAhIAAAMCEgAAAwISAAADAhIAAAMCEgAAAwISAAADAhIAAAMCEgAAAwISAAADAhIAAAMCEgAAAwISAAADAZGegHR7ne/+11UzBlt87JX5r3a54zkvP2FQ1U10ouIlGAwKImJiZFeBgDgCgQCAXG73b1+Xf6KFQAAAwISAAADAhIAAAMCEgAAAwISAACDkAKyqKhIbr31VrnuuuskNTVVZs2aJfX19baas2fPypIlS2TIkCEyaNAgue+++6S5udlW09jYKPn5+ZKQkCCpqalSUFAgnZ2dtpry8nKZPHmyuFwuGTt2rGzYsOGi9RQXF8vIkSMlLi5OcnNz5ZNPPgllOwAAXJqGwOfz6fr167W2tlZramr05z//uQ4fPlxPnTpl1SxevFgzMzO1tLRU9+3bpz/60Y/0xz/+sXW+s7NTJ0yYoHl5eVpdXa3bt2/XlJQULSwstGq+/PJLTUhI0GXLlunhw4f1lVde0QEDBuiOHTusmo0bN6rT6dTXX39dDx06pAsXLtSkpCRtbm7u8X4CgYCKCIPBYDCu4hEIBEKJsh4LKSD/v5aWFhUR3bVrl6qqtra2amxsrG7evNmqqaurUxHRyspKVVXdvn27xsTEqN/vt2rWrl2rbrdb29vbVVX1qaee0uzsbNtcc+bMUZ/PZz2+7bbbdMmSJdbj8+fPa0ZGhhYVFfV4/QQkg8FgXP0jXAF5Rd+DDAQCIiIyePBgERGpqqqSjo4OycvLs2rGjx8vw4cPl8rKShERqayslJycHElLS7NqfD6fBINBOXTokFVz4TW6a7qvce7cOamqqrLVxMTESF5enlVj0t7eLsFg0DYAADD53gHZ1dUlTz75pNx+++0yYcIEERHx+/3idDolKSnJVpuWliZ+v9+quTAcu893n7tcTTAYlDNnzsjXX38t58+fN9Z0X8OkqKhIEhMTrZGZmRn6xgEAUeF7B+SSJUuktrZWNm7c2JvrCavCwkIJBALWOH78eKSXBADop77XDytfunSpvPfee1JRUSHXX3+9ddzj8ci5c+ektbXV9i6yublZPB6PVfP/7zbtvsv1wpr/f+drc3OzuN1uiY+PlwEDBsiAAQOMNd3XMHG5XOJyuULfMAAg6oT0DlJVZenSpbJlyxbZuXOnjBo1ynZ+ypQpEhsbK6Wlpdax+vp6aWxsFK/XKyIiXq9XDh48KC0tLVZNSUmJuN1uufHGG62aC6/RXdN9DafTKVOmTLHVdHV1SWlpqVUDAMAVCeWOnkcffVQTExO1vLxcm5qarHH69GmrZvHixTp8+HDduXOn7tu3T71er3q9Xut898c8pk+frjU1Nbpjxw4dOnSo8WMeBQUFWldXp8XFxcaPebhcLt2wYYMePnxYH3nkEU1KSrLdHftduIuVwWAwrv7RLz7mcanFrV+/3qo5c+aMPvbYY5qcnKwJCQl67733alNTk+06R48e1ZkzZ2p8fLympKTo8uXLtaOjw1ZTVlamkyZNUqfTqaNHj7bN0e2VV17R4cOHq9Pp1Ntuu00//vjjULZDQDIYDMY1MMIVkPw+SH4fJABc1fh9kGEQxf9vAADXjHC9lkd1QJ44cSLSSwAAXKG2trawXPd7fczjWtH9E4AaGxv5q9YwCgaDkpmZKcePHw/LX4Pgb+hz36DPfee7eq2q0tbWJhkZGWGZP6oDMibmb2+gExMT+YPeB9xuN33uA/S5b9DnvnO5XofzzU1U/xUrAACXQkACAGAQ1QHpcrlk5cqV/Pi5MKPPfYM+9w363Hci3euo/hwkAACXEtXvIAEAuBQCEgAAAwISAAADAhIAAAMCEgAAg6gNyOLiYhk5cqTExcVJbm6ufPLJJ5FeUr/17LPPisPhsI3x48db58+ePStLliyRIUOGyKBBg+S+++6T5uZm2zUaGxslPz9fEhISJDU1VQoKCqSzs9NWU15eLpMnTxaXyyVjx46VDRs29MX2IqqiokLuuusuycjIEIfDIVu3brWdV1V55plnJD09XeLj4yUvL08+//xzW83Jkydl3rx54na7JSkpSRYsWCCnTp2y1Rw4cECmTp0qcXFxkpmZKatXr75oLZs3b5bx48dLXFyc5OTkyPbt23t9v5HyXX1+8MEHL/ozPmPGDFsNff5uRUVFcuutt8p1110nqampMmvWLKmvr7fV9OXrxRW/zofll2j1cxs3blSn06mvv/66Hjp0SBcuXKhJSUna3Nwc6aX1SytXrtTs7GzbL8n+61//ap1fvHixZmZmamlpqe7bt09/9KMf6Y9//GPrfPcvyc7Ly9Pq6mrdvn27pqSkGH9J9rJly/Tw4cP6yiuvXPRLsq9F27dv13/7t3/Td955R0VEt2zZYju/atUqTUxM1K1bt+r+/fv17rvv1lGjRumZM2esmhkzZujEiRP1448/1j/96U86duxYnTt3rnU+EAhoWlqazps3T2tra/Xtt9/W+Ph4XbdunVWze/duHTBggK5evVoPHz6s//7v/66xsbF68ODBsPegL3xXn+fPn68zZsyw/Rk/efKkrYY+fzefz6fr16/X2tparamp0Z///Oc6fPhwPXXqlFXTV68XvfE6H5UBedttt+mSJUusx+fPn9eMjAwtKiqK4Kr6r5UrV+rEiRON51pbWzU2NlY3b95sHaurq1MR0crKSlX924tTTEyM+v1+q2bt2rXqdru1vb1dVVWfeuopzc7Otl17zpw56vP5enk3/df/f+Hu6upSj8eja9assY61traqy+XSt99+W1VVDx8+rCKin376qVXz/vvvq8Ph0K+++kpVVV999VVNTk62eq2qumLFCs3KyrIez549W/Pz823ryc3N1UWLFvXqHvuDSwXkPffcc8nn0Ofvp6WlRUVEd+3apap9+3rRG6/zUfdXrOfOnZOqqirJy8uzjsXExEheXp5UVlZGcGX92+e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+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "ename": "",
+     "evalue": "",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[1;31mLe noyau s’est bloqué lors de l’exécution du code dans une cellule active ou une cellule précédente. \n",
+      "\u001b[1;31mVeuillez vérifier le code dans la ou les cellules pour identifier une cause possible de l’échec. \n",
+      "\u001b[1;31mCliquez <a href='https://aka.ms/vscodeJupyterKernelCrash'>ici</a> pour plus d’informations. \n",
+      "\u001b[1;31mPour plus d’informations, consultez Jupyter <a href='command:jupyter.viewOutput'>log</a>."
+     ]
+    }
+   ],
+   "source": [
+    "def generate_image(nx, ny, periods=6.25, threshold=0.45, radius=.9):\n",
+    "    X, Y = np.meshgrid(np.linspace(-1, 1, nx, endpoint=True), np.linspace(-1, 1, ny, endpoint=True))\n",
+    "    image = (np.cos(2*np.pi*X*periods) > threshold)*1.\n",
+    "    # image += (np.cos(2*np.pi*Y*periods) > threshold)*1.\n",
+    "    # image = (image>=1) * 1.\n",
+    "    image *= (X**2 < radius**2) * (Y**2 < radius**2) * 1.\n",
+    "    return image\n",
+    "image = generate_image(nx=c.opt.nx, ny=c.opt.ny)\n",
+    "plt.imshow(image, cmap='gray');"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "self.cachepath='/tmp/2024-07-15_caustique-Granet'\n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [44:51<00:00, 33.22s/it]\n",
+      "100%|██████████| 1/1 [44:51<00:00, 2691.02s/it]\n",
+      "  0%|          | 0/1 [00:00<?, ?it/s]"
+     ]
+    }
+   ],
+   "source": [
+    "c = Caustique(init())\n",
+    "c.opt.tag = f'{c.opt.figpath}-{PRECISION=}'\n",
+    "output_filename = c.plot(z, image)\n",
+    "pprint(output_filename)\n",
+    "# c.show(output_filename)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "c.show(output_filename)"
+   ]
+  }
+ ],
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+  "kernelspec": {
+   "display_name": "Python 3.10.6 ('stim')",
+   "language": "python",
+   "name": "python3"
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+   "mimetype": "text/x-python",
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diff --git a/2024-07-15_caustique-Granet.py b/2024-07-15_caustique-Granet.py
new file mode 100644
index 0000000..c10c230
--- /dev/null
+++ b/2024-07-15_caustique-Granet.py
@@ -0,0 +1,275 @@
+import os
+import numpy as np
+
+# the higher PRECISION, the bigger the file
+# PRECISION = 4  # debugging
+# PRECISION = 10 # good quality
+PRECISION = 12 # for production
+PRECISION = 13 # for production
+
+# https://docs.python.org/3/library/dataclasses.html?highlight=dataclass#module-dataclasses
+from dataclasses import dataclass
+
+@dataclass
+class init:
+    figpath: str = '2024-07-15_caustique-Granet' # Folder to store images
+    phi: float = 1.61803 # beauty is gold
+    tag: str = 'caustique' # Tag
+    ext: str = 'png' # Extension for output
+    nx: int = 5*2**PRECISION # number of pixels (vertical)
+    ny: int = 5*2**PRECISION # number of pixels (horizontal)
+    nframe: int = 1 # number of frames
+    bin_dens: int = 1 # relative bin density
+    bin_spectrum: int = 1 # bin spacing in spectrum (lower is more CPU)
+    seed: int = 2024 # seed for RNG
+    H: float = 20.0 # depth of the pool
+    variation: float = .20 # variation of diffraction index: http://www.philiplaven.com/p20.html 1.40 at 400 nm and 1.37 at 700nm makes a 2% variation
+    scale: float = .50*2**PRECISION # period in pixels
+    B_sf: float = 0.75 # bandwidth in sf
+    V_Y: float = 0.3 # horizontal speed
+    V_X: float = 0.3 # vertical speed
+    B_V: float = 1.0 # bandwidth in speed
+    zmin: float = 0.2 # gradient of wave height
+    # theta: float = 2*np.pi*(2-1.61803) # angle with the horizontal
+    theta: float = np.pi/2 # angle with the horizontal
+    B_theta: float = 60*np.pi/180 # bandwidth in theta
+    min_lum: float = .1 # diffusion level for the rendering
+    gamma: float = 2.9 # Gamma exponant to convert luminosity to luminance
+    fps: float = 18 # frames per second
+    multispectral: bool = True # Compute caustics on the full spectrogram.
+    cache: bool = True # Cache intermediate output.
+    verbose: bool = True # Displays more verbose output.
+    do_display: bool = False # Displays images in notebook.
+    do_recompute: bool = True # Restart each computation    
+
+
+from lambda2color import Lambda2color, xyz_from_xy
+
+# borrowed from https://github.com/gummiks/gummiks.github.io/blob/master/scripts/astro/planck.py
+def planck(wav, T):
+    import scipy.constants as const
+    c = const.c # c = 3.0e+8
+    h = const.h # h = 6.626e-34
+    k = const.k # k = 1.38e-23
+    a = 2.0*h*c**2
+    b = h*c/(wav*k*T)
+    intensity = a / ( (wav**5) * (np.exp(b) - 1.0) )
+    return intensity
+
+def scattering(wav, a=0.005, p=1.3, b=0.45):
+    """
+    b is  proportionate  to  the  column  density  of  aerosols
+    along  the  path  of  sunlight,  from  outside  the  atmosphere
+    to  the  point  of  observation
+    
+    see https://laurentperrinet.github.io/sciblog/posts/2020-07-04-colors-of-the-sky.html for more details
+
+    """
+    # converting wav in µm:
+    intensity = np.exp(-a/((wav/1e-6)**4)) # Rayleigh extinction by nitrogen
+    intensity *= (wav/1e-6)**-4
+    intensity *= np.exp(-b/((wav/1e-6)**p)) # Aerosols
+    return intensity
+
+import matplotlib
+import matplotlib.pyplot as plt
+from tqdm import tqdm, trange
+import shutil
+import hashlib
+import MotionClouds as mc
+
+class Caustique:
+    def __init__(self, opt):
+        """
+        Image coordinates follow 'ij' indexing, that is,
+        * their origin at the top left,
+        * the X axis is vertical and goes "down",
+        * the Y axis is horizontal and goes "right".
+
+        """
+        self.mc = mc
+        self.ratio = opt.ny/opt.nx # ratio between height and width (>1 for portrait, <1 for landscape)
+        X = np.linspace(0, 1, opt.nx, endpoint=False) # vertical
+        Y = np.linspace(0, self.ratio, opt.ny, endpoint=False) # horizontal
+        self.xv, self.yv = np.meshgrid(X, Y, indexing='ij')
+        self.opt = opt
+        # https://stackoverflow.com/questions/16878315/what-is-the-right-way-to-treat-python-argparse-namespace-as-a-dictionary
+        self.d = vars(opt)
+        os.makedirs(self.opt.figpath, exist_ok=True)
+        self.cachepath = os.path.join('/tmp', self.opt.figpath)
+        if opt.verbose: print(f'{self.cachepath=}')
+        os.makedirs(self.cachepath, exist_ok=True)
+
+        # a standard white:
+        # illuminant_D65 = xyz_from_xy(0.3127, 0.3291), 
+        illuminant_sun = xyz_from_xy(0.325998, 0.335354)
+        # color conversion class
+        self.cs_srgb = Lambda2color(red=xyz_from_xy(0.64, 0.33),
+                               green=xyz_from_xy(0.30, 0.60),
+                               blue=xyz_from_xy(0.15, 0.06),
+                               white=illuminant_sun)
+        self.wavelengths = self.cs_srgb.cmf[:, 0]*1e-9
+        self.N_wavelengths = len(self.wavelengths)
+        # multiply by the spectrum of the sky
+        intensity5800 = planck(self.wavelengths, 5800.)
+        scatter = scattering(self.wavelengths)
+        self.spectrum_sky = intensity5800 * scatter
+        self.spectrum_sky /= self.spectrum_sky.max()
+
+    def wave(self):
+        filename = f'{self.cachepath}/{self.opt.tag}_wave.npy'
+        if os.path.isfile(filename) and not(self.opt.do_recompute):
+            z = np.load(filename)
+        else:
+            # A simplistic model of a wave using https://github.com/NeuralEnsemble/MotionClouds
+            fx, fy, ft = mc.get_grids(self.opt.nx, self.opt.ny, self.opt.nframe)
+            env = mc.envelope_gabor(fx, fy, ft, V_X=self.opt.V_Y, V_Y=self.opt.V_X, B_V=self.opt.B_V,
+                                    sf_0=1./self.opt.scale, B_sf=self.opt.B_sf/self.opt.scale,
+                                    theta=self.opt.theta, B_theta=self.opt.B_theta)
+            z = mc.rectif(mc.random_cloud(env, seed=self.opt.seed))
+            if self.opt.cache: np.save(filename, z)
+        return z * np.linspace(self.opt.zmin, 1., self.opt.nx)[:, None, None]
+
+    def transform(self, z_, modulation=1.):
+        xv, yv = self.xv.copy(), self.yv.copy()
+
+        dzdx = z_ - np.roll(z_, 1, axis=0)
+        dzdy = z_ - np.roll(z_, 1, axis=1)
+        xv = xv + modulation * self.opt.H * dzdx
+        yv = yv + modulation * self.opt.H * dzdy
+
+        xv = np.mod(xv, 1)
+        yv = np.mod(yv, self.ratio)
+
+        return xv, yv
+
+    def plot(self, z, image=None, do_color=True, dpi=50):
+        """
+        
+        dpi: output resolution - sets the figure size as we ensure there is a one to one correspondance between pixels in the data and the output image
+        """
+
+        # output filename        
+        md5 = hashlib.sha224((self.opt.figpath + self.opt.tag).encode()).hexdigest()[:8] # an unique identifier for future tagging
+        output_filename = f'{self.opt.figpath}/{self.opt.tag}_{md5}.{self.opt.ext}'
+        if os.path.isfile(output_filename) and not(self.opt.do_recompute):
+            return output_filename
+        else:
+            # 1/ do the raytracing of image through z:
+            binsx, binsy = self.opt.nx//self.opt.bin_dens, self.opt.ny//self.opt.bin_dens
+
+            # a fixed image in degree of contrast (from 0=black to 1=white)
+            if image is None: image = np.ones((self.opt.nx, self.opt.ny))
+
+            #hist = self.do_raytracing(z)
+            # binsx, binsy = self.opt.nx//self.opt.bin_dens, self.opt.ny//self.opt.bin_dens
+
+            subplotpars = matplotlib.figure.SubplotParams(left=0., right=1., bottom=0., top=1., wspace=0., hspace=0.,)
+
+            if self.opt.multispectral:
+
+                #image_rgb = self.cs_srgb.spec_to_rgb(hist)
+                image_rgb = np.zeros((self.opt.nx//self.opt.bin_dens,  self.opt.ny//self.opt.bin_dens, 3, self.opt.nframe))
+                for i_frame in trange(self.opt.nframe):
+                    for i_wavelength in trange(self.opt.bin_spectrum//2, self.N_wavelengths, self.opt.bin_spectrum):
+                        modulation = 1. + self.opt.variation/2 - self.opt.variation*i_wavelength/self.N_wavelengths
+                        xv, yv = self.transform(z[:, :, i_frame], modulation=modulation)
+                        hist_, _, _ = np.histogram2d(xv.ravel(), yv.ravel(),
+                                                     bins=[binsx, binsy],
+                                                     weights=image.ravel(),
+                                                     range=[[0, 1], [0, self.ratio]],
+                                                     density=True)
+
+                        # we convert the spectrum into a color
+                        spec = np.zeros((self.N_wavelengths))
+                        spec[i_wavelength] = 1
+                        rgb = self.cs_srgb.spec_to_rgb(spec)
+                        rgb *= self.spectrum_sky[i_wavelength]
+                        # we add the color to the image
+                        image_rgb[:, :, :, i_frame] += hist_[:, :, None] * rgb[None, None, :]
+
+                image_rgb -= image_rgb.min()
+                image_rgb /= image_rgb.max()
+            else:
+                hist = np.zeros((binsx, binsy, self.opt.nframe))
+                for i_frame in trange(self.opt.nframe):
+                    xv, yv = self.transform(z[:, :, i_frame])
+                    hist_, _, _ = np.histogram2d(xv.ravel(), yv.ravel(),
+                                                        bins=[binsx, binsy],
+                                                        range=[[0, 1], [0, self.ratio]],
+                                                        density=True)
+                #hist /= hist.max()
+
+            # 2/ transform light into image:
+            fnames = []
+            for i_frame in trange(self.opt.nframe):
+                fig, ax = plt.subplots(figsize=(self.opt.ny/self.opt.bin_dens/dpi, self.opt.nx/self.opt.bin_dens/dpi), subplotpars=subplotpars)
+                if self.opt.multispectral:
+                    ax.imshow(image_rgb[:, :, :, i_frame] ** (1/self.opt.gamma), vmin=0, vmax=1)
+                else:
+                    if do_color:
+                        bluesky = np.array([0.268375, 0.283377]) # xyz
+                        sun = np.array([0.325998, 0.335354]) # xyz
+                        # ax.pcolormesh(edge_y, edge_x, hist[:, :, i_frame], vmin=0, vmax=1, cmap=plt.cm.Blues_r)
+                        # https://en.wikipedia.org/wiki/CIE_1931_color_space#Mixing_colors_specified_with_the_CIE_xy_chromaticity_diagram
+                        L1 = 1 - hist[:, :, i_frame]
+                        L2 = hist[:, :, i_frame]
+                        image_denom = L1 / bluesky[1] + L2 / sun[1]
+                        image_x = (L1 * bluesky[0] / bluesky[1] + L2 * sun[0] / sun[1]) / image_denom
+                        image_y = (L1 + L2) / image_denom 
+                        image_xyz = np.dstack((image_x, image_y, 1 - image_x - image_y))
+                        image_rgb = self.cs_srgb.xyz_to_rgb(image_xyz)
+                        image_L = self.opt.min_lum + (1-self.opt.min_lum)* L2 ** .61803
+                        ax.imshow(image_L[:, :, None]*image_rgb, vmin=0, vmax=1)
+
+                    else:
+                        ax.imshow(1-image_L, vmin=0, vmax=1)
+
+                fname = f'{self.cachepath}/{self.opt.tag}_frame_{i_frame:04d}.png'
+                fig.savefig(fname, dpi=dpi)
+                fnames.append(fname)
+                plt.close('all')
+
+            if self.opt.nframe==1:
+                shutil.copyfile(fname, output_filename)
+                return output_filename
+            else:
+                if self.opt.ext == 'gif':
+                    return make_gif(output_filename, fnames, fps=self.opt.fps)
+                else:
+                    return make_mp4(output_filename, fnames, fps=self.opt.fps)
+
+    def show(self, output_filename, width=1024):
+        from IPython.display import HTML, Image, display
+        if self.opt.nframe==1:
+            display(Image(url=output_filename.replace(self.opt.ext, 'png'), width=width))
+        else:
+            if self.opt.ext == 'gif':
+                return display(Image(url=output_filename, width=width))
+            else:
+                #import moviepy.editor as mpy
+                #return mpy.ipython_display(output_filename, width=width)
+                # https://github.com/NeuralEnsemble/MotionClouds/blob/master/MotionClouds/MotionClouds.py#L858
+                opts = ' loop="1" autoplay="1" controls '
+                html = HTML(f'<video {opts} width="{width}"> <source src="{output_filename}" type="video/{self.opt.ext}" />  </video>')
+                html.reload()
+                return display(html)
+            
+
+def generate_image(nx, ny, periods=6.25, threshold=0.45, radius=.9):
+    X, Y = np.meshgrid(np.linspace(-1, 1, nx, endpoint=True), np.linspace(-1, 1, ny, endpoint=True))
+    image = (np.cos(2*np.pi*X*periods) > threshold)*1.
+    # image += (np.cos(2*np.pi*Y*periods) > threshold)*1.
+    # image = (image>=1) * 1.
+    image *= (X**2 < radius**2) * (Y**2 < radius**2) * 1.
+    return image
+
+opt = init()
+
+c = Caustique(opt)
+c.opt.tag = f'{c.opt.figpath}-{PRECISION=}'
+z = c.wave()
+image = generate_image(nx=c.opt.nx, ny=c.opt.ny)
+output_filename = c.plot(z, image)
+print(output_filename)
+print('Done !')
\ No newline at end of file
diff --git a/2024-07-15_caustique.ipynb b/2024-07-15_caustique.ipynb
new file mode 100644
index 0000000..2e05b58
--- /dev/null
+++ b/2024-07-15_caustique.ipynb
@@ -0,0 +1,4696 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Caustics"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:17.668239Z",
+     "iopub.status.busy": "2022-09-16T06:50:17.667940Z",
+     "iopub.status.idle": "2022-09-16T06:50:17.670759Z",
+     "shell.execute_reply": "2022-09-16T06:50:17.670294Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "import os\n",
+    "import numpy as np\n",
+    "\n",
+    "# the higher PRECISION, the bigger the file\n",
+    "# PRECISION = 4  # debugging\n",
+    "PRECISION = 10 # good quality\n",
+    "# PRECISION = 14 # for production\n",
+    "\n",
+    "# https://docs.python.org/3/library/dataclasses.html?highlight=dataclass#module-dataclasses\n",
+    "from dataclasses import dataclass\n",
+    "\n",
+    "@dataclass\n",
+    "class init:\n",
+    "    figpath: str = '2024-07-14_caustique' # Folder to store images\n",
+    "    phi: float = 1.61803 # beauty is gold\n",
+    "    tag: str = 'caustique' # Tag\n",
+    "    ext: str = 'png' # Extension for output\n",
+    "    nx: int = 5*2**PRECISION # number of pixels (vertical)\n",
+    "    ny: int = 5*2**PRECISION # number of pixels (horizontal)\n",
+    "    nframe: int = 1 # number of frames\n",
+    "    bin_dens: int = 1 # relative bin density\n",
+    "    bin_spectrum: int = 1 # bin spacing in spectrum (lower is more CPU)\n",
+    "    seed: int = 2024 # seed for RNG\n",
+    "    H: float = 20.0 # depth of the pool\n",
+    "    variation: float = .20 # variation of diffraction index: http://www.philiplaven.com/p20.html 1.40 at 400 nm and 1.37 at 700nm makes a 2% variation\n",
+    "    scale: float = .50*2**PRECISION # period in pixels\n",
+    "    B_sf: float = 0.75 # bandwidth in sf\n",
+    "    V_Y: float = 0.3 # horizontal speed\n",
+    "    V_X: float = 0.3 # vertical speed\n",
+    "    B_V: float = 1.0 # bandwidth in speed\n",
+    "    zmin: float = 0.2 # gradient of wave height\n",
+    "    # theta: float = 2*np.pi*(2-1.61803) # angle with the horizontal\n",
+    "    theta: float = np.pi/2 # angle with the horizontal\n",
+    "    B_theta: float = 60*np.pi/180 # bandwidth in theta\n",
+    "    min_lum: float = .1 # diffusion level for the rendering\n",
+    "    gamma: float = 2.9 # Gamma exponant to convert luminosity to luminance\n",
+    "    fps: float = 18 # frames per second\n",
+    "    multispectral: bool = True # Compute caustics on the full spectrogram.\n",
+    "    cache: bool = True # Cache intermediate output.\n",
+    "    verbose: bool = False # Displays more verbose output.\n",
+    "    do_display: bool = False # Displays images in notebook.\n",
+    "    do_recompute: bool = False # Restart each computation    "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:17.688713Z",
+     "iopub.status.busy": "2022-09-16T06:50:17.688504Z",
+     "iopub.status.idle": "2022-09-16T06:50:17.691583Z",
+     "shell.execute_reply": "2022-09-16T06:50:17.691125Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Saving our simulations in=2024-07-14_caustique\n"
+     ]
+    }
+   ],
+   "source": [
+    "opt = init()\n",
+    "print(f'Saving our simulations in={opt.figpath}')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "if opt.nframe==1: opt.ext = 'png'"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:17.728359Z",
+     "iopub.status.busy": "2022-09-16T06:50:17.728155Z",
+     "iopub.status.idle": "2022-09-16T06:50:17.734829Z",
+     "shell.execute_reply": "2022-09-16T06:50:17.734354Z"
+    },
+    "tags": []
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "init(figpath='2024-07-14_caustique',\n",
+      "     phi=1.61803,\n",
+      "     tag='caustique',\n",
+      "     ext='png',\n",
+      "     nx=5120,\n",
+      "     ny=5120,\n",
+      "     nframe=1,\n",
+      "     bin_dens=1,\n",
+      "     bin_spectrum=1,\n",
+      "     seed=2024,\n",
+      "     H=20.0,\n",
+      "     variation=0.2,\n",
+      "     scale=512.0,\n",
+      "     B_sf=0.75,\n",
+      "     V_Y=0.3,\n",
+      "     V_X=0.3,\n",
+      "     B_V=1.0,\n",
+      "     zmin=0.2,\n",
+      "     theta=1.5707963267948966,\n",
+      "     B_theta=1.0471975511965976,\n",
+      "     min_lum=0.1,\n",
+      "     gamma=2.9,\n",
+      "     fps=18,\n",
+      "     multispectral=True,\n",
+      "     cache=True,\n",
+      "     verbose=False,\n",
+      "     do_display=False,\n",
+      "     do_recompute=False)\n"
+     ]
+    }
+   ],
+   "source": [
+    "from pprint import pprint\n",
+    "pprint(opt)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## utilities\n",
+    "\n",
+    "Transfoming a sequence of PNG frames into gif or mp4:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:17.737334Z",
+     "iopub.status.busy": "2022-09-16T06:50:17.737126Z",
+     "iopub.status.idle": "2022-09-16T06:50:17.741165Z",
+     "shell.execute_reply": "2022-09-16T06:50:17.740716Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "def make_gif(gifname, fnames, fps, do_delete=True):\n",
+    "    import imageio\n",
+    "\n",
+    "    with imageio.get_writer(gifname, mode='I', fps=fps) as writer:\n",
+    "        for fname in fnames:\n",
+    "            writer.append_data(imageio.imread(fname))\n",
+    "\n",
+    "    from pygifsicle import optimize\n",
+    "    optimize(str(gifname))\n",
+    "    if do_delete: \n",
+    "        for fname in fnames: os.remove(fname)\n",
+    "    return gifname\n",
+    "\n",
+    "# https://moviepy.readthedocs.io/en/latest/getting_started/videoclips.html#imagesequenceclip\n",
+    "def make_mp4(mp4name, fnames, fps, do_delete=True):\n",
+    "    import moviepy.editor as mpy\n",
+    "    clip = mpy.ImageSequenceClip(fnames, fps=fps)\n",
+    "    clip.write_videofile(mp4name, fps=fps, codec='libx264', verbose=False, logger=None)\n",
+    "    if do_delete: \n",
+    "        for fname in fnames: os.remove(fname)\n",
+    "    return mp4name"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "\n",
+    "Utilities to compute the spectrum of the blue sky and convert them later to RGB values (check out https://laurentperrinet.github.io/sciblog/posts/2020-07-04-colors-of-the-sky.html for details)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:17.743669Z",
+     "iopub.status.busy": "2022-09-16T06:50:17.743461Z",
+     "iopub.status.idle": "2022-09-16T06:50:17.757701Z",
+     "shell.execute_reply": "2022-09-16T06:50:17.757282Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "from lambda2color import Lambda2color, xyz_from_xy\n",
+    "\n",
+    "# borrowed from https://github.com/gummiks/gummiks.github.io/blob/master/scripts/astro/planck.py\n",
+    "def planck(wav, T):\n",
+    "    import scipy.constants as const\n",
+    "    c = const.c # c = 3.0e+8\n",
+    "    h = const.h # h = 6.626e-34\n",
+    "    k = const.k # k = 1.38e-23\n",
+    "    a = 2.0*h*c**2\n",
+    "    b = h*c/(wav*k*T)\n",
+    "    intensity = a / ( (wav**5) * (np.exp(b) - 1.0) )\n",
+    "    return intensity\n",
+    "\n",
+    "def scattering(wav, a=0.005, p=1.3, b=0.45):\n",
+    "    \"\"\"\n",
+    "    b is  proportionate  to  the  column  density  of  aerosols\n",
+    "    along  the  path  of  sunlight,  from  outside  the  atmosphere\n",
+    "    to  the  point  of  observation\n",
+    "    \n",
+    "    see https://laurentperrinet.github.io/sciblog/posts/2020-07-04-colors-of-the-sky.html for more details\n",
+    "\n",
+    "    \"\"\"\n",
+    "    # converting wav in µm:\n",
+    "    intensity = np.exp(-a/((wav/1e-6)**4)) # Rayleigh extinction by nitrogen\n",
+    "    intensity *= (wav/1e-6)**-4\n",
+    "    intensity *= np.exp(-b/((wav/1e-6)**p)) # Aerosols\n",
+    "    return intensity"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## computing the caustics"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:17.012647Z",
+     "iopub.status.busy": "2022-09-16T06:50:17.012413Z",
+     "iopub.status.idle": "2022-09-16T06:50:17.665184Z",
+     "shell.execute_reply": "2022-09-16T06:50:17.664652Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "<>:181: SyntaxWarning: invalid escape sequence '\\>'\n",
+      "<>:181: SyntaxWarning: invalid escape sequence '\\>'\n",
+      "/var/folders/3p/m0g52j9j69z3gj8ktpgg1dm00000gn/T/ipykernel_72879/3587749359.py:181: SyntaxWarning: invalid escape sequence '\\>'\n",
+      "  html = HTML(f'<video {opts} src=\"{output_filename}\" type=\"video/{self.opt.ext}\" width={width}\\>')\n"
+     ]
+    }
+   ],
+   "source": [
+    "import matplotlib\n",
+    "import matplotlib.pyplot as plt\n",
+    "from tqdm import tqdm, trange\n",
+    "import shutil\n",
+    "import hashlib\n",
+    "import MotionClouds as mc\n",
+    "\n",
+    "class Caustique:\n",
+    "    def __init__(self, opt):\n",
+    "        \"\"\"\n",
+    "        Image coordinates follow 'ij' indexing, that is,\n",
+    "        * their origin at the top left,\n",
+    "        * the X axis is vertical and goes \"down\",\n",
+    "        * the Y axis is horizontal and goes \"right\".\n",
+    "\n",
+    "        \"\"\"\n",
+    "        self.mc = mc\n",
+    "        self.ratio = opt.ny/opt.nx # ratio between height and width (>1 for portrait, <1 for landscape)\n",
+    "        X = np.linspace(0, 1, opt.nx, endpoint=False) # vertical\n",
+    "        Y = np.linspace(0, self.ratio, opt.ny, endpoint=False) # horizontal\n",
+    "        self.xv, self.yv = np.meshgrid(X, Y, indexing='ij')\n",
+    "        self.opt = opt\n",
+    "        # https://stackoverflow.com/questions/16878315/what-is-the-right-way-to-treat-python-argparse-namespace-as-a-dictionary\n",
+    "        self.d = vars(opt)\n",
+    "        os.makedirs(self.opt.figpath, exist_ok=True)\n",
+    "        self.cachepath = os.path.join('/tmp', self.opt.figpath)\n",
+    "        if opt.verbose: print(f'{self.cachepath=}')\n",
+    "        os.makedirs(self.cachepath, exist_ok=True)\n",
+    "\n",
+    "        # a standard white:\n",
+    "        # illuminant_D65 = xyz_from_xy(0.3127, 0.3291), \n",
+    "        illuminant_sun = xyz_from_xy(0.325998, 0.335354)\n",
+    "        # color conversion class\n",
+    "        self.cs_srgb = Lambda2color(red=xyz_from_xy(0.64, 0.33),\n",
+    "                               green=xyz_from_xy(0.30, 0.60),\n",
+    "                               blue=xyz_from_xy(0.15, 0.06),\n",
+    "                               white=illuminant_sun)\n",
+    "        self.wavelengths = self.cs_srgb.cmf[:, 0]*1e-9\n",
+    "        self.N_wavelengths = len(self.wavelengths)\n",
+    "        # multiply by the spectrum of the sky\n",
+    "        intensity5800 = planck(self.wavelengths, 5800.)\n",
+    "        scatter = scattering(self.wavelengths)\n",
+    "        self.spectrum_sky = intensity5800 * scatter\n",
+    "        self.spectrum_sky /= self.spectrum_sky.max()\n",
+    "\n",
+    "    def wave(self):\n",
+    "        filename = f'{self.cachepath}/{self.opt.tag}_wave.npy'\n",
+    "        if os.path.isfile(filename) and not(self.opt.do_recompute):\n",
+    "            z = np.load(filename)\n",
+    "        else:\n",
+    "            # A simplistic model of a wave using https://github.com/NeuralEnsemble/MotionClouds\n",
+    "            fx, fy, ft = mc.get_grids(self.opt.nx, self.opt.ny, self.opt.nframe)\n",
+    "            env = mc.envelope_gabor(fx, fy, ft, V_X=self.opt.V_Y, V_Y=self.opt.V_X, B_V=self.opt.B_V,\n",
+    "                                    sf_0=1./self.opt.scale, B_sf=self.opt.B_sf/self.opt.scale,\n",
+    "                                    theta=self.opt.theta, B_theta=self.opt.B_theta)\n",
+    "            z = mc.rectif(mc.random_cloud(env, seed=self.opt.seed))\n",
+    "            if self.opt.cache: np.save(filename, z)\n",
+    "        return z * np.linspace(self.opt.zmin, 1., self.opt.nx)[:, None, None]\n",
+    "\n",
+    "    def transform(self, z_, modulation=1.):\n",
+    "        xv, yv = self.xv.copy(), self.yv.copy()\n",
+    "\n",
+    "        dzdx = z_ - np.roll(z_, 1, axis=0)\n",
+    "        dzdy = z_ - np.roll(z_, 1, axis=1)\n",
+    "        xv = xv + modulation * self.opt.H * dzdx\n",
+    "        yv = yv + modulation * self.opt.H * dzdy\n",
+    "\n",
+    "        xv = np.mod(xv, 1)\n",
+    "        yv = np.mod(yv, self.ratio)\n",
+    "\n",
+    "        return xv, yv\n",
+    "\n",
+    "    def plot(self, z, image=None, do_color=True, dpi=50):\n",
+    "        \"\"\"\n",
+    "        \n",
+    "        dpi: output resolution - sets the figure size as we ensure there is a one to one correspondance between pixels in the data and the output image\n",
+    "        \"\"\"\n",
+    "\n",
+    "        # output filename        \n",
+    "        md5 = hashlib.sha224((self.opt.figpath + self.opt.tag).encode()).hexdigest()[:8] # an unique identifier for future tagging\n",
+    "        output_filename = f'{self.opt.figpath}/{self.opt.tag}_{md5}.{self.opt.ext}'\n",
+    "        if os.path.isfile(output_filename) and not(self.opt.do_recompute):\n",
+    "            return output_filename\n",
+    "        else:\n",
+    "            # 1/ do the raytracing of image through z:\n",
+    "            binsx, binsy = self.opt.nx//self.opt.bin_dens, self.opt.ny//self.opt.bin_dens\n",
+    "\n",
+    "            # a fixed image in degree of contrast (from 0=black to 1=white)\n",
+    "            if image is None: image = np.ones((self.opt.nx, self.opt.ny))\n",
+    "\n",
+    "            #hist = self.do_raytracing(z)\n",
+    "            binsx, binsy = self.opt.nx//self.opt.bin_dens, self.opt.ny//self.opt.bin_dens\n",
+    "\n",
+    "            subplotpars = matplotlib.figure.SubplotParams(left=0., right=1., bottom=0., top=1., wspace=0., hspace=0.,)\n",
+    "\n",
+    "            if self.opt.multispectral:\n",
+    "\n",
+    "                #image_rgb = self.cs_srgb.spec_to_rgb(hist)\n",
+    "                image_rgb = np.zeros((self.opt.nx//self.opt.bin_dens,  self.opt.ny//self.opt.bin_dens, 3, self.opt.nframe))\n",
+    "                for i_frame in trange(self.opt.nframe):\n",
+    "                    for i_wavelength in trange(self.opt.bin_spectrum//2, self.N_wavelengths, self.opt.bin_spectrum):\n",
+    "                        modulation = 1. + self.opt.variation/2 - self.opt.variation*i_wavelength/self.N_wavelengths\n",
+    "                        xv, yv = self.transform(z[:, :, i_frame], modulation=modulation)\n",
+    "                        hist_, _, _ = np.histogram2d(xv.ravel(), yv.ravel(),\n",
+    "                                                     bins=[binsx, binsy],\n",
+    "                                                     weights=image.ravel(),\n",
+    "                                                     range=[[0, 1], [0, self.ratio]],\n",
+    "                                                     density=True)\n",
+    "\n",
+    "                        # we convert the spectrum into a color\n",
+    "                        spec = np.zeros((self.N_wavelengths))\n",
+    "                        spec[i_wavelength] = 1\n",
+    "                        rgb = self.cs_srgb.spec_to_rgb(spec)\n",
+    "                        rgb *= self.spectrum_sky[i_wavelength]\n",
+    "                        # we add the color to the image\n",
+    "                        image_rgb[:, :, :, i_frame] += hist_[:, :, None] * rgb[None, None, :]\n",
+    "\n",
+    "                image_rgb -= image_rgb.min()\n",
+    "                image_rgb /= image_rgb.max()\n",
+    "            else:\n",
+    "                hist = np.zeros((binsx, binsy, self.opt.nframe))\n",
+    "                for i_frame in trange(self.opt.nframe):\n",
+    "                    xv, yv = self.transform(z[:, :, i_frame])\n",
+    "                    hist_, _, _ = np.histogram2d(xv.ravel(), yv.ravel(),\n",
+    "                                                        bins=[binsx, binsy],\n",
+    "                                                        range=[[0, 1], [0, self.ratio]],\n",
+    "                                                        density=True)\n",
+    "                #hist /= hist.max()\n",
+    "\n",
+    "            # 2/ transform light into image:\n",
+    "            fnames = []\n",
+    "            for i_frame in trange(self.opt.nframe):\n",
+    "                fig, ax = plt.subplots(figsize=(self.opt.ny/self.opt.bin_dens/dpi, self.opt.nx/self.opt.bin_dens/dpi), subplotpars=subplotpars)\n",
+    "                if self.opt.multispectral:\n",
+    "                    ax.imshow(image_rgb[:, :, :, i_frame] ** (1/self.opt.gamma), vmin=0, vmax=1)\n",
+    "                else:\n",
+    "                    if do_color:\n",
+    "                        bluesky = np.array([0.268375, 0.283377]) # xyz\n",
+    "                        sun = np.array([0.325998, 0.335354]) # xyz\n",
+    "                        # ax.pcolormesh(edge_y, edge_x, hist[:, :, i_frame], vmin=0, vmax=1, cmap=plt.cm.Blues_r)\n",
+    "                        # https://en.wikipedia.org/wiki/CIE_1931_color_space#Mixing_colors_specified_with_the_CIE_xy_chromaticity_diagram\n",
+    "                        L1 = 1 - hist[:, :, i_frame]\n",
+    "                        L2 = hist[:, :, i_frame]\n",
+    "                        image_denom = L1 / bluesky[1] + L2 / sun[1]\n",
+    "                        image_x = (L1 * bluesky[0] / bluesky[1] + L2 * sun[0] / sun[1]) / image_denom\n",
+    "                        image_y = (L1 + L2) / image_denom \n",
+    "                        image_xyz = np.dstack((image_x, image_y, 1 - image_x - image_y))\n",
+    "                        image_rgb = self.cs_srgb.xyz_to_rgb(image_xyz)\n",
+    "                        image_L = self.opt.min_lum + (1-self.opt.min_lum)* L2 ** .61803\n",
+    "                        ax.imshow(image_L[:, :, None]*image_rgb, vmin=0, vmax=1)\n",
+    "\n",
+    "                    else:\n",
+    "                        ax.imshow(1-image_L, vmin=0, vmax=1)\n",
+    "\n",
+    "                fname = f'{self.cachepath}/{self.opt.tag}_frame_{i_frame:04d}.png'\n",
+    "                fig.savefig(fname, dpi=dpi)\n",
+    "                fnames.append(fname)\n",
+    "                plt.close('all')\n",
+    "\n",
+    "            if self.opt.nframe==1:\n",
+    "                shutil.copyfile(fname, output_filename)\n",
+    "                return output_filename\n",
+    "            else:\n",
+    "                if self.opt.ext == 'gif':\n",
+    "                    return make_gif(output_filename, fnames, fps=self.opt.fps)\n",
+    "                else:\n",
+    "                    return make_mp4(output_filename, fnames, fps=self.opt.fps)\n",
+    "\n",
+    "    def show(self, output_filename, width=1024):\n",
+    "        from IPython.display import HTML, Image, display\n",
+    "        if self.opt.nframe==1:\n",
+    "            display(Image(url=output_filename.replace(self.opt.ext, 'png'), width=width))\n",
+    "        else:\n",
+    "            if self.opt.ext == 'gif':\n",
+    "                return display(Image(url=output_filename, width=width))\n",
+    "            else:\n",
+    "                #import moviepy.editor as mpy\n",
+    "                #return mpy.ipython_display(output_filename, width=width)\n",
+    "                # https://github.com/NeuralEnsemble/MotionClouds/blob/master/MotionClouds/MotionClouds.py#L858\n",
+    "                opts = ' loop=\"1\" autoplay=\"1\" controls '\n",
+    "                html = HTML(f'<video {opts} src=\"{output_filename}\" type=\"video/{self.opt.ext}\" width={width}\\>')\n",
+    "                html.reload()\n",
+    "                return display(html)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# a simple caustics"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "tags": []
+   },
+   "source": [
+    "## generating the caustics"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:17.864888Z",
+     "iopub.status.busy": "2022-09-16T06:50:17.864663Z",
+     "iopub.status.idle": "2022-09-16T06:50:19.896847Z",
+     "shell.execute_reply": "2022-09-16T06:50:19.896285Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(5120, 5120, 1)"
+      ]
+     },
+     "execution_count": 8,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "c = Caustique(opt)\n",
+    "z = c.wave()\n",
+    "z.shape"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:19.899518Z",
+     "iopub.status.busy": "2022-09-16T06:50:19.899287Z",
+     "iopub.status.idle": "2022-09-16T06:50:19.902454Z",
+     "shell.execute_reply": "2022-09-16T06:50:19.902008Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "c = Caustique(opt)\n",
+    "output_filename = c.plot(z)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:19.904998Z",
+     "iopub.status.busy": "2022-09-16T06:50:19.904782Z",
+     "iopub.status.idle": "2022-09-16T06:50:19.908171Z",
+     "shell.execute_reply": "2022-09-16T06:50:19.907731Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<img src=\"2024-07-14_caustique/caustique_ae282e1b.png\" width=\"1024\"/>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Image object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "c.show(output_filename)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "tags": []
+   },
+   "source": [
+    "# exploring parameters"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:19.910794Z",
+     "iopub.status.busy": "2022-09-16T06:50:19.910587Z",
+     "iopub.status.idle": "2022-09-16T06:50:19.913072Z",
+     "shell.execute_reply": "2022-09-16T06:50:19.912580Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "N_scan = 9\n",
+    "base = 2"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "tags": []
+   },
+   "source": [
+    "## water depth"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
+     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
+     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
+     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "H = 10.000 -> output_filename='2024-07-14_caustique/caustique_H_10.000_ae34f7ad.png' \n",
+      "H = 11.892 -> output_filename='2024-07-14_caustique/caustique_H_11.892_b4752ed2.png' \n",
+      "H = 14.142 -> output_filename='2024-07-14_caustique/caustique_H_14.142_74ead794.png' \n",
+      "H = 16.818 -> output_filename='2024-07-14_caustique/caustique_H_16.818_8e13a8c2.png' \n",
+      "H = 20.000 -> output_filename='2024-07-14_caustique/caustique_H_20.000_8f854c6a.png' \n",
+      "H = 23.784 -> output_filename='2024-07-14_caustique/caustique_H_23.784_a7a69d8d.png' \n",
+      "H = 28.284 -> output_filename='2024-07-14_caustique/caustique_H_28.284_f2053472.png' \n",
+      "H = 33.636 -> output_filename='2024-07-14_caustique/caustique_H_33.636_d4063bd4.png' \n",
+      "H = 40.000 -> output_filename='2024-07-14_caustique/caustique_H_40.000_0f2bfcc5.png' \n"
+     ]
+    }
+   ],
+   "source": [
+    "for H_ in c.opt.H*np.logspace(-1, 1, N_scan, base=base):\n",
+    "    opt = init()\n",
+    "    c = Caustique(opt)\n",
+    "    c.opt.H = H_\n",
+    "    c.opt.tag = f'{c.opt.tag}_H_{H_:.3f}'\n",
+    "    \n",
+    "    output_filename = c.plot(z)\n",
+    "    print(f'H = {H_:.3f} -> {output_filename=} ')\n",
+    "    if c.opt.do_display: c.show(output_filename)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "tags": []
+   },
+   "source": [
+    "## refraction index variation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:21.644704Z",
+     "iopub.status.busy": "2022-09-16T06:50:21.644457Z",
+     "iopub.status.idle": "2022-09-16T06:50:23.391217Z",
+     "shell.execute_reply": "2022-09-16T06:50:23.390608Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "variation = 0.010  -> output_filename='2024-07-14_caustique/caustique_variation_0.010_2da01962.png'\n",
+      "variation = 0.017  -> output_filename='2024-07-14_caustique/caustique_variation_0.017_23fdd42d.png'\n",
+      "variation = 0.028  -> output_filename='2024-07-14_caustique/caustique_variation_0.028_0f96adeb.png'\n",
+      "variation = 0.046  -> output_filename='2024-07-14_caustique/caustique_variation_0.046_590e72b0.png'\n",
+      "variation = 0.077  -> output_filename='2024-07-14_caustique/caustique_variation_0.077_578269e5.png'\n",
+      "variation = 0.129  -> output_filename='2024-07-14_caustique/caustique_variation_0.129_27227cf5.png'\n",
+      "variation = 0.215  -> output_filename='2024-07-14_caustique/caustique_variation_0.215_dccf4840.png'\n",
+      "variation = 0.359  -> output_filename='2024-07-14_caustique/caustique_variation_0.359_ab2dfc52.png'\n",
+      "variation = 0.599  -> output_filename='2024-07-14_caustique/caustique_variation_0.599_a80b9e15.png'\n"
+     ]
+    }
+   ],
+   "source": [
+    "for variation_ in np.logspace(-2, 0, N_scan, base=10, endpoint=False):\n",
+    "    opt = init()\n",
+    "    c = Caustique(opt)\n",
+    "    c.opt.variation = variation_\n",
+    "    c.opt.tag = f'{opt.tag}_variation_{variation_:.3f}'\n",
+    "\n",
+    "    output_filename = c.plot(z)\n",
+    "    print(f'variation = {variation_:.3f}  -> {output_filename=}')\n",
+    "    if c.opt.do_display: c.show(output_filename)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "tags": []
+   },
+   "source": [
+    "## other variables on the wave"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:23.394466Z",
+     "iopub.status.busy": "2022-09-16T06:50:23.394219Z",
+     "iopub.status.idle": "2022-09-16T06:50:23.686162Z",
+     "shell.execute_reply": "2022-09-16T06:50:23.685512Z"
+    },
+    "tags": []
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "======scale======\n",
+      "scale=scale(default)*0.500=2.560E+02 -> output_filename='2024-07-14_caustique/caustique_scale_modul_0.500_c604344d.png'\n",
+      "scale=scale(default)*0.595=3.044E+02 -> output_filename='2024-07-14_caustique/caustique_scale_modul_0.595_8a118e1b.png'\n",
+      "scale=scale(default)*0.707=3.620E+02 -> output_filename='2024-07-14_caustique/caustique_scale_modul_0.707_5127207e.png'\n",
+      "scale=scale(default)*0.841=4.305E+02 -> output_filename='2024-07-14_caustique/caustique_scale_modul_0.841_b93d1acd.png'\n",
+      "scale=scale(default)*1.000=5.120E+02 -> output_filename='2024-07-14_caustique/caustique_scale_modul_1.000_4726be6c.png'\n",
+      "scale=scale(default)*1.189=6.089E+02 -> output_filename='2024-07-14_caustique/caustique_scale_modul_1.189_efe6ea66.png'\n",
+      "scale=scale(default)*1.414=7.241E+02 -> output_filename='2024-07-14_caustique/caustique_scale_modul_1.414_37b568f3.png'\n",
+      "scale=scale(default)*1.682=8.611E+02 -> output_filename='2024-07-14_caustique/caustique_scale_modul_1.682_9931385e.png'\n",
+      "scale=scale(default)*2.000=1.024E+03 -> output_filename='2024-07-14_caustique/caustique_scale_modul_2.000_cbb3c4e4.png'\n",
+      "======B_sf======\n",
+      "B_sf=B_sf(default)*0.500=3.750E-01 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_0.500_383b4351.png'\n",
+      "B_sf=B_sf(default)*0.595=4.460E-01 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_0.595_95951377.png'\n",
+      "B_sf=B_sf(default)*0.707=5.303E-01 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_0.707_7c3540c0.png'\n",
+      "B_sf=B_sf(default)*0.841=6.307E-01 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_0.841_a9575ac6.png'\n",
+      "B_sf=B_sf(default)*1.000=7.500E-01 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_1.000_8f4e5737.png'\n",
+      "B_sf=B_sf(default)*1.189=8.919E-01 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_1.189_d2b25845.png'\n",
+      "B_sf=B_sf(default)*1.414=1.061E+00 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_1.414_2f17ce4e.png'\n",
+      "B_sf=B_sf(default)*1.682=1.261E+00 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_1.682_df4a6f79.png'\n",
+      "B_sf=B_sf(default)*2.000=1.500E+00 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_2.000_4098d1cb.png'\n",
+      "======theta======\n",
+      "theta=theta(default)*0.500=7.854E-01 -> output_filename='2024-07-14_caustique/caustique_theta_modul_0.500_242027b1.png'\n",
+      "theta=theta(default)*0.595=9.340E-01 -> output_filename='2024-07-14_caustique/caustique_theta_modul_0.595_e550294b.png'\n",
+      "theta=theta(default)*0.707=1.111E+00 -> output_filename='2024-07-14_caustique/caustique_theta_modul_0.707_7277b68e.png'\n",
+      "theta=theta(default)*0.841=1.321E+00 -> output_filename='2024-07-14_caustique/caustique_theta_modul_0.841_b73e0a2e.png'\n",
+      "theta=theta(default)*1.000=1.571E+00 -> output_filename='2024-07-14_caustique/caustique_theta_modul_1.000_cf424ffc.png'\n"
+     ]
+    }
+   ],
+   "source": [
+    "for variable in ['scale', 'B_sf', 'theta',  'B_theta', 'gamma', 'min_lum', 'zmin']: #  'V_Y', 'V_X', 'B_V', \n",
+    "    print(f'======{variable}======')\n",
+    "    for modul in np.logspace(-1, 1, N_scan, base=base):\n",
+    "        opt = init()\n",
+    "        c = Caustique(opt)\n",
+    "        c.d[variable] *= modul\n",
+    "        c.opt.tag = f'{c.opt.tag}_{variable}_modul_{modul:.3f}'\n",
+    "        \n",
+    "        z = c.wave()\n",
+    "        output_filename = c.plot(z)\n",
+    "        print(f'{variable}={variable}(default)*{modul:.3f}={c.d[variable]:.3E} -> {output_filename=}')\n",
+    "        if c.opt.do_display: c.show(output_filename)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## shining a grating image to the wave"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "type = 'grating'"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "def generate_image(nx, ny, periods=6.25, threshold=0.45, radius=.9):\n",
+    "    X, Y = np.meshgrid(np.linspace(-1, 1, nx, endpoint=True), np.linspace(-1, 1, ny, endpoint=True))\n",
+    "    image = (np.cos(2*np.pi*X*periods) > threshold)*1.\n",
+    "    # image += (np.cos(2*np.pi*Y*periods) > threshold)*1.\n",
+    "    # image = (image>=1) * 1.\n",
+    "    image *= (X**2 < radius**2) * (Y**2 < radius**2) * 1.\n",
+    "    return image\n",
+    "image = generate_image(nx=c.opt.nx, ny=c.opt.ny)\n",
+    "plt.imshow(image, cmap='gray');"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<img src=\"2024-07-14_caustique/caustique_grating-image_0f4d6abd.png\" width=\"1024\"/>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Image object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "c = Caustique(init())\n",
+    "c.opt.tag = f'{c.opt.tag}_{type}-image'\n",
+    "output_filename = c.plot(z, image)\n",
+    "c.show(output_filename)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "H = 10.000 -> output_filename='2024-07-14_caustique/caustique_grating-image_H_10.000_ad40f238.png' \n",
+      "H = 11.892 -> output_filename='2024-07-14_caustique/caustique_grating-image_H_11.892_74cee302.png' \n",
+      "H = 14.142 -> output_filename='2024-07-14_caustique/caustique_grating-image_H_14.142_a7a1b4de.png' \n",
+      "H = 16.818 -> output_filename='2024-07-14_caustique/caustique_grating-image_H_16.818_403d723f.png' \n",
+      "H = 20.000 -> output_filename='2024-07-14_caustique/caustique_grating-image_H_20.000_ea3ebcb9.png' \n",
+      "H = 23.784 -> output_filename='2024-07-14_caustique/caustique_grating-image_H_23.784_8d4ecd03.png' \n",
+      "H = 28.284 -> output_filename='2024-07-14_caustique/caustique_grating-image_H_28.284_ee4904bf.png' \n",
+      "H = 33.636 -> output_filename='2024-07-14_caustique/caustique_grating-image_H_33.636_dee9e852.png' \n",
+      "H = 40.000 -> output_filename='2024-07-14_caustique/caustique_grating-image_H_40.000_1e5e805b.png' \n"
+     ]
+    }
+   ],
+   "source": [
+    "for H_ in c.opt.H*np.logspace(-1, 1, N_scan, base=base):\n",
+    "    opt = init()\n",
+    "    c = Caustique(opt)\n",
+    "    c.opt.H = H_\n",
+    "    c.opt.tag = f'{c.opt.tag}_{type}-image_H_{H_:.3f}'\n",
+    "    \n",
+    "    output_filename = c.plot(z, image)\n",
+    "    print(f'H = {H_:.3f} -> {output_filename=} ')\n",
+    "    if c.opt.do_display: c.show(output_filename)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.100 -> output_filename='2024-07-14_caustique/caustique_grating-image_threshold=0.100_a3c1b385.png' \n",
+      "0.200 -> output_filename='2024-07-14_caustique/caustique_grating-image_threshold=0.200_4e55756a.png' \n",
+      "0.300 -> output_filename='2024-07-14_caustique/caustique_grating-image_threshold=0.300_d1092b03.png' \n",
+      "0.400 -> output_filename='2024-07-14_caustique/caustique_grating-image_threshold=0.400_992d2572.png' \n",
+      "0.500 -> output_filename='2024-07-14_caustique/caustique_grating-image_threshold=0.500_0dc18b43.png' \n",
+      "0.600 -> output_filename='2024-07-14_caustique/caustique_grating-image_threshold=0.600_5a21681f.png' \n",
+      "0.700 -> output_filename='2024-07-14_caustique/caustique_grating-image_threshold=0.700_0c00edac.png' \n",
+      "0.800 -> output_filename='2024-07-14_caustique/caustique_grating-image_threshold=0.800_3043c558.png' \n",
+      "0.900 -> output_filename='2024-07-14_caustique/caustique_grating-image_threshold=0.900_ff5af108.png' \n"
+     ]
+    }
+   ],
+   "source": [
+    "for threshold in np.linspace(0, 1, N_scan+2, endpoint=True)[1:-1]:\n",
+    "    opt = init()\n",
+    "    c = Caustique(opt)\n",
+    "\n",
+    "    c.opt.tag = f'{c.opt.tag}_{type}-image_{threshold=:.3f}'\n",
+    "    image = generate_image(nx=c.opt.nx, ny=c.opt.ny, threshold=threshold)\n",
+    "    output_filename = c.plot(z, image)\n",
+    "    print(f'{threshold:.3f} -> {output_filename=} ')\n",
+    "    if c.opt.do_display: c.show(output_filename)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "radius=0.111 -> output_filename='2024-07-14_caustique/caustique_grating-image_radius=0.111_506f42be.png' \n",
+      "radius=0.222 -> output_filename='2024-07-14_caustique/caustique_grating-image_radius=0.222_2093ce00.png' \n",
+      "radius=0.333 -> output_filename='2024-07-14_caustique/caustique_grating-image_radius=0.333_2c311f7e.png' \n",
+      "radius=0.444 -> output_filename='2024-07-14_caustique/caustique_grating-image_radius=0.444_f2cc585a.png' \n",
+      "radius=0.556 -> output_filename='2024-07-14_caustique/caustique_grating-image_radius=0.556_02219953.png' \n",
+      "radius=0.667 -> output_filename='2024-07-14_caustique/caustique_grating-image_radius=0.667_8abb8845.png' \n",
+      "radius=0.778 -> output_filename='2024-07-14_caustique/caustique_grating-image_radius=0.778_8069def4.png' \n",
+      "radius=0.889 -> output_filename='2024-07-14_caustique/caustique_grating-image_radius=0.889_8490256a.png' \n",
+      "radius=1.000 -> output_filename='2024-07-14_caustique/caustique_grating-image_radius=1.000_17e95f27.png' \n"
+     ]
+    }
+   ],
+   "source": [
+    "for radius in np.linspace(0, 1, N_scan+1)[1:]:\n",
+    "    opt = init()\n",
+    "    c = Caustique(opt)\n",
+    "\n",
+    "    c.opt.tag = f'{c.opt.tag}_{type}-image_{radius=:.3f}'\n",
+    "    image = generate_image(nx=c.opt.nx, ny=c.opt.ny, radius=radius)\n",
+    "    output_filename = c.plot(z, image)\n",
+    "    print(f'{radius=:.3f} -> {output_filename=} ')\n",
+    "    if c.opt.do_display: c.show(output_filename)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "periods=1.000 -> output_filename='2024-07-14_caustique/caustique_grating-image_periods=1.00e+00_398f3b6a.png' \n",
+      "periods=1.334 -> output_filename='2024-07-14_caustique/caustique_grating-image_periods=1.33e+00_ead8222a.png' \n",
+      "periods=1.778 -> output_filename='2024-07-14_caustique/caustique_grating-image_periods=1.78e+00_e5410dfb.png' \n",
+      "periods=2.371 -> output_filename='2024-07-14_caustique/caustique_grating-image_periods=2.37e+00_b922972a.png' \n",
+      "periods=3.162 -> output_filename='2024-07-14_caustique/caustique_grating-image_periods=3.16e+00_620eccdf.png' \n",
+      "periods=4.217 -> output_filename='2024-07-14_caustique/caustique_grating-image_periods=4.22e+00_599aff90.png' \n",
+      "periods=5.623 -> output_filename='2024-07-14_caustique/caustique_grating-image_periods=5.62e+00_e09f7302.png' \n",
+      "periods=7.499 -> output_filename='2024-07-14_caustique/caustique_grating-image_periods=7.50e+00_b3344e7c.png' \n",
+      "periods=10.000 -> output_filename='2024-07-14_caustique/caustique_grating-image_periods=1.00e+01_248ef1c2.png' \n"
+     ]
+    }
+   ],
+   "source": [
+    "for periods in np.logspace(0, 1, N_scan, base=10):\n",
+    "    opt = init()\n",
+    "    c = Caustique(opt)\n",
+    "\n",
+    "    c.opt.tag = f'{c.opt.tag}_{type}-image_{periods=:.2e}'\n",
+    "    image = generate_image(nx=c.opt.nx, ny=c.opt.ny, periods=periods)\n",
+    "    output_filename = c.plot(z, image)\n",
+    "    print(f'{periods=:.3f} -> {output_filename=} ')\n",
+    "    if c.opt.do_display: c.show(output_filename)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "======scale======\n",
+      "scale=scale(default)*0.500=2.560E+02 -> output_filename='2024-07-14_caustique/caustique_scale_modul_0.500_c604344d.png'\n",
+      "scale=scale(default)*0.595=3.044E+02 -> output_filename='2024-07-14_caustique/caustique_scale_modul_0.595_8a118e1b.png'\n",
+      "scale=scale(default)*0.707=3.620E+02 -> output_filename='2024-07-14_caustique/caustique_scale_modul_0.707_5127207e.png'\n",
+      "scale=scale(default)*0.841=4.305E+02 -> output_filename='2024-07-14_caustique/caustique_scale_modul_0.841_b93d1acd.png'\n",
+      "scale=scale(default)*1.000=5.120E+02 -> output_filename='2024-07-14_caustique/caustique_scale_modul_1.000_4726be6c.png'\n",
+      "scale=scale(default)*1.189=6.089E+02 -> output_filename='2024-07-14_caustique/caustique_scale_modul_1.189_efe6ea66.png'\n",
+      "scale=scale(default)*1.414=7.241E+02 -> output_filename='2024-07-14_caustique/caustique_scale_modul_1.414_37b568f3.png'\n",
+      "scale=scale(default)*1.682=8.611E+02 -> output_filename='2024-07-14_caustique/caustique_scale_modul_1.682_9931385e.png'\n",
+      "scale=scale(default)*2.000=1.024E+03 -> output_filename='2024-07-14_caustique/caustique_scale_modul_2.000_cbb3c4e4.png'\n",
+      "======B_sf======\n",
+      "B_sf=B_sf(default)*0.500=3.750E-01 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_0.500_383b4351.png'\n",
+      "B_sf=B_sf(default)*0.595=4.460E-01 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_0.595_95951377.png'\n",
+      "B_sf=B_sf(default)*0.707=5.303E-01 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_0.707_7c3540c0.png'\n",
+      "B_sf=B_sf(default)*0.841=6.307E-01 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_0.841_a9575ac6.png'\n",
+      "B_sf=B_sf(default)*1.000=7.500E-01 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_1.000_8f4e5737.png'\n",
+      "B_sf=B_sf(default)*1.189=8.919E-01 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_1.189_d2b25845.png'\n",
+      "B_sf=B_sf(default)*1.414=1.061E+00 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_1.414_2f17ce4e.png'\n",
+      "B_sf=B_sf(default)*1.682=1.261E+00 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_1.682_df4a6f79.png'\n",
+      "B_sf=B_sf(default)*2.000=1.500E+00 -> output_filename='2024-07-14_caustique/caustique_B_sf_modul_2.000_4098d1cb.png'\n",
+      "======theta======\n",
+      "theta=theta(default)*0.500=7.854E-01 -> output_filename='2024-07-14_caustique/caustique_theta_modul_0.500_242027b1.png'\n",
+      "theta=theta(default)*0.595=9.340E-01 -> output_filename='2024-07-14_caustique/caustique_theta_modul_0.595_e550294b.png'\n",
+      "theta=theta(default)*0.707=1.111E+00 -> output_filename='2024-07-14_caustique/caustique_theta_modul_0.707_7277b68e.png'\n",
+      "theta=theta(default)*0.841=1.321E+00 -> output_filename='2024-07-14_caustique/caustique_theta_modul_0.841_b73e0a2e.png'\n",
+      "theta=theta(default)*1.000=1.571E+00 -> output_filename='2024-07-14_caustique/caustique_theta_modul_1.000_cf424ffc.png'\n",
+      "theta=theta(default)*1.189=1.868E+00 -> output_filename='2024-07-14_caustique/caustique_theta_modul_1.189_7c2a3a4b.png'\n",
+      "theta=theta(default)*1.414=2.221E+00 -> output_filename='2024-07-14_caustique/caustique_theta_modul_1.414_938b2f5e.png'\n",
+      "theta=theta(default)*1.682=2.642E+00 -> output_filename='2024-07-14_caustique/caustique_theta_modul_1.682_155a3f39.png'\n",
+      "theta=theta(default)*2.000=3.142E+00 -> output_filename='2024-07-14_caustique/caustique_theta_modul_2.000_0f2224e2.png'\n",
+      "======B_theta======\n",
+      "B_theta=B_theta(default)*0.500=5.236E-01 -> output_filename='2024-07-14_caustique/caustique_B_theta_modul_0.500_b1ee37cc.png'\n",
+      "B_theta=B_theta(default)*0.595=6.227E-01 -> output_filename='2024-07-14_caustique/caustique_B_theta_modul_0.595_981305cc.png'\n",
+      "B_theta=B_theta(default)*0.707=7.405E-01 -> output_filename='2024-07-14_caustique/caustique_B_theta_modul_0.707_e6118a37.png'\n",
+      "B_theta=B_theta(default)*0.841=8.806E-01 -> output_filename='2024-07-14_caustique/caustique_B_theta_modul_0.841_a39c1030.png'\n",
+      "B_theta=B_theta(default)*1.000=1.047E+00 -> output_filename='2024-07-14_caustique/caustique_B_theta_modul_1.000_b8eab39d.png'\n",
+      "B_theta=B_theta(default)*1.189=1.245E+00 -> output_filename='2024-07-14_caustique/caustique_B_theta_modul_1.189_b4c01f0c.png'\n",
+      "B_theta=B_theta(default)*1.414=1.481E+00 -> output_filename='2024-07-14_caustique/caustique_B_theta_modul_1.414_955c5dde.png'\n",
+      "B_theta=B_theta(default)*1.682=1.761E+00 -> output_filename='2024-07-14_caustique/caustique_B_theta_modul_1.682_d79ba197.png'\n",
+      "B_theta=B_theta(default)*2.000=2.094E+00 -> output_filename='2024-07-14_caustique/caustique_B_theta_modul_2.000_f7453e38.png'\n",
+      "======gamma======\n",
+      "gamma=gamma(default)*0.500=1.450E+00 -> output_filename='2024-07-14_caustique/caustique_gamma_modul_0.500_ba6d5d7c.png'\n",
+      "gamma=gamma(default)*0.595=1.724E+00 -> output_filename='2024-07-14_caustique/caustique_gamma_modul_0.595_943b676e.png'\n",
+      "gamma=gamma(default)*0.707=2.051E+00 -> output_filename='2024-07-14_caustique/caustique_gamma_modul_0.707_2a4d88b2.png'\n",
+      "gamma=gamma(default)*0.841=2.439E+00 -> output_filename='2024-07-14_caustique/caustique_gamma_modul_0.841_8449735a.png'\n",
+      "gamma=gamma(default)*1.000=2.900E+00 -> output_filename='2024-07-14_caustique/caustique_gamma_modul_1.000_9dda329f.png'\n",
+      "gamma=gamma(default)*1.189=3.449E+00 -> output_filename='2024-07-14_caustique/caustique_gamma_modul_1.189_76347b5f.png'\n",
+      "gamma=gamma(default)*1.414=4.101E+00 -> output_filename='2024-07-14_caustique/caustique_gamma_modul_1.414_e416938f.png'\n",
+      "gamma=gamma(default)*1.682=4.877E+00 -> output_filename='2024-07-14_caustique/caustique_gamma_modul_1.682_e1a4096e.png'\n",
+      "gamma=gamma(default)*2.000=5.800E+00 -> output_filename='2024-07-14_caustique/caustique_gamma_modul_2.000_a89910d3.png'\n",
+      "======min_lum======\n",
+      "min_lum=min_lum(default)*0.500=5.000E-02 -> output_filename='2024-07-14_caustique/caustique_min_lum_modul_0.500_78f7d01a.png'\n",
+      "min_lum=min_lum(default)*0.595=5.946E-02 -> output_filename='2024-07-14_caustique/caustique_min_lum_modul_0.595_f4033056.png'\n",
+      "min_lum=min_lum(default)*0.707=7.071E-02 -> output_filename='2024-07-14_caustique/caustique_min_lum_modul_0.707_e8313869.png'\n",
+      "min_lum=min_lum(default)*0.841=8.409E-02 -> output_filename='2024-07-14_caustique/caustique_min_lum_modul_0.841_ec324732.png'\n",
+      "min_lum=min_lum(default)*1.000=1.000E-01 -> output_filename='2024-07-14_caustique/caustique_min_lum_modul_1.000_12d0eee9.png'\n",
+      "min_lum=min_lum(default)*1.189=1.189E-01 -> output_filename='2024-07-14_caustique/caustique_min_lum_modul_1.189_059343b5.png'\n",
+      "min_lum=min_lum(default)*1.414=1.414E-01 -> output_filename='2024-07-14_caustique/caustique_min_lum_modul_1.414_c48ebc27.png'\n",
+      "min_lum=min_lum(default)*1.682=1.682E-01 -> output_filename='2024-07-14_caustique/caustique_min_lum_modul_1.682_497c3bfd.png'\n",
+      "min_lum=min_lum(default)*2.000=2.000E-01 -> output_filename='2024-07-14_caustique/caustique_min_lum_modul_2.000_2ec2ab1f.png'\n",
+      "======zmin======\n",
+      "zmin=zmin(default)*0.500=1.000E-01 -> output_filename='2024-07-14_caustique/caustique_zmin_modul_0.500_76289697.png'\n",
+      "zmin=zmin(default)*0.595=1.189E-01 -> output_filename='2024-07-14_caustique/caustique_zmin_modul_0.595_384a4243.png'\n",
+      "zmin=zmin(default)*0.707=1.414E-01 -> output_filename='2024-07-14_caustique/caustique_zmin_modul_0.707_1f61d862.png'\n",
+      "zmin=zmin(default)*0.841=1.682E-01 -> output_filename='2024-07-14_caustique/caustique_zmin_modul_0.841_d2a0b0c9.png'\n",
+      "zmin=zmin(default)*1.000=2.000E-01 -> output_filename='2024-07-14_caustique/caustique_zmin_modul_1.000_5ce3c1db.png'\n",
+      "zmin=zmin(default)*1.189=2.378E-01 -> output_filename='2024-07-14_caustique/caustique_zmin_modul_1.189_10d93ccb.png'\n",
+      "zmin=zmin(default)*1.414=2.828E-01 -> output_filename='2024-07-14_caustique/caustique_zmin_modul_1.414_2d132a18.png'\n",
+      "zmin=zmin(default)*1.682=3.364E-01 -> output_filename='2024-07-14_caustique/caustique_zmin_modul_1.682_7e5ce573.png'\n",
+      "zmin=zmin(default)*2.000=4.000E-01 -> output_filename='2024-07-14_caustique/caustique_zmin_modul_2.000_a27f6770.png'\n"
+     ]
+    }
+   ],
+   "source": [
+    "for variable in ['scale', 'B_sf', 'theta',  'B_theta', 'gamma', 'min_lum', 'zmin']: #  'V_Y', 'V_X', 'B_V', \n",
+    "    print(f'======{variable}======')\n",
+    "    for modul in np.logspace(-1, 1, N_scan, base=base):\n",
+    "        opt = init()\n",
+    "        c = Caustique(opt)\n",
+    "        c.d[variable] *= modul\n",
+    "        c.opt.tag = f'{c.opt.tag}_{variable}_modul_{modul:.3f}'\n",
+    "        z = c.wave()\n",
+    "        image = generate_image(nx=c.opt.nx, ny=c.opt.ny)\n",
+    "        output_filename = c.plot(z, image)\n",
+    "        print(f'{variable}={variable}(default)*{modul:.3f}={c.d[variable]:.3E} -> {output_filename=}')\n",
+    "        if c.opt.do_display: c.show(output_filename)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "tags": []
+   },
+   "source": [
+    "## shining a grid image to the wave"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "type = 'grid'"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "def generate_image(nx, ny, periods=10, threshold=0.45, radius=.9):\n",
+    "    X, Y = np.meshgrid(np.linspace(-1, 1, nx, endpoint=True), np.linspace(-1, 1, ny, endpoint=True))\n",
+    "    image = (np.cos(2*np.pi*X*periods) > threshold)*1.\n",
+    "    image += (np.cos(2*np.pi*Y*periods) > threshold)*1.\n",
+    "    image = (image>=1) * 1.\n",
+    "    image *= ((X**2 + Y**2) < radius**2) * 1.\n",
+    "    return image\n",
+    "    \n",
+    "image = generate_image(nx=c.opt.nx, ny=c.opt.ny, periods=10, threshold=0.45, radius=.9)\n",
+    "plt.imshow(image, cmap='gray');"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<img src=\"2024-07-14_caustique/caustique_grid-image_3b042836.png\" width=\"1024\"/>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Image object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "c = Caustique(init())\n",
+    "c.opt.tag = f'{c.opt.tag}_{type}-image'\n",
+    "\n",
+    "output_filename = c.plot(z, image)\n",
+    "c.show(output_filename)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
+     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
+     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
+     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "threshold=0.100 -> output_filename='2024-07-14_caustique/caustique_grid-image_threshold=0.100_d3898cb2.png' \n",
+      "threshold=0.200 -> output_filename='2024-07-14_caustique/caustique_grid-image_threshold=0.200_d725e91c.png' \n",
+      "threshold=0.300 -> output_filename='2024-07-14_caustique/caustique_grid-image_threshold=0.300_69d58422.png' \n",
+      "threshold=0.400 -> output_filename='2024-07-14_caustique/caustique_grid-image_threshold=0.400_33b6ec67.png' \n",
+      "threshold=0.500 -> output_filename='2024-07-14_caustique/caustique_grid-image_threshold=0.500_876672bd.png' \n",
+      "threshold=0.600 -> output_filename='2024-07-14_caustique/caustique_grid-image_threshold=0.600_8284a303.png' \n",
+      "threshold=0.700 -> output_filename='2024-07-14_caustique/caustique_grid-image_threshold=0.700_8e369d08.png' \n",
+      "threshold=0.800 -> output_filename='2024-07-14_caustique/caustique_grid-image_threshold=0.800_0e3a91a8.png' \n",
+      "threshold=0.900 -> output_filename='2024-07-14_caustique/caustique_grid-image_threshold=0.900_c2317ac6.png' \n"
+     ]
+    }
+   ],
+   "source": [
+    "for threshold in np.linspace(0, 1, N_scan+2, endpoint=True)[1:-1]:\n",
+    "    opt = init()\n",
+    "    c = Caustique(opt)\n",
+    "\n",
+    "    c.opt.tag = f'{c.opt.tag}_{type}-image_{threshold=:.3f}'\n",
+    "    image = generate_image(nx=c.opt.nx, ny=c.opt.ny, periods=10, threshold=threshold)\n",
+    "    output_filename = c.plot(z, image)\n",
+    "    print(f'{threshold=:.3f} -> {output_filename=} ')\n",
+    "    if c.opt.do_display: c.show(output_filename)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
+     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
+     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
+     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "H = 10.000 -> output_filename='2024-07-14_caustique/caustique_grid-image_H_10.000_ee4aa4eb.png' \n",
+      "H = 11.892 -> output_filename='2024-07-14_caustique/caustique_grid-image_H_11.892_3ed2289e.png' \n",
+      "H = 14.142 -> output_filename='2024-07-14_caustique/caustique_grid-image_H_14.142_671eaed7.png' \n",
+      "H = 16.818 -> output_filename='2024-07-14_caustique/caustique_grid-image_H_16.818_93af91ea.png' \n",
+      "H = 20.000 -> output_filename='2024-07-14_caustique/caustique_grid-image_H_20.000_ea2a5518.png' \n",
+      "H = 23.784 -> output_filename='2024-07-14_caustique/caustique_grid-image_H_23.784_d1747c22.png' \n",
+      "H = 28.284 -> output_filename='2024-07-14_caustique/caustique_grid-image_H_28.284_09e14169.png' \n",
+      "H = 33.636 -> output_filename='2024-07-14_caustique/caustique_grid-image_H_33.636_6146eac8.png' \n",
+      "H = 40.000 -> output_filename='2024-07-14_caustique/caustique_grid-image_H_40.000_4da793a1.png' \n"
+     ]
+    }
+   ],
+   "source": [
+    "for H_ in c.opt.H*np.logspace(-1, 1, N_scan, base=base):\n",
+    "    opt = init()\n",
+    "    c = Caustique(opt)\n",
+    "    c.opt.H = H_\n",
+    "    c.opt.tag = f'{c.opt.tag}_{type}-image_H_{H_:.3f}'\n",
+    "    \n",
+    "    output_filename = c.plot(z, image)\n",
+    "    print(f'H = {H_:.3f} -> {output_filename=} ')\n",
+    "    if c.opt.do_display: c.show(output_filename)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
+     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
+     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
+     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "periods=1.000 -> output_filename='2024-07-14_caustique/caustique_grid-image_periods=1.000_31de32b4.png' \n",
+      "periods=1.334 -> output_filename='2024-07-14_caustique/caustique_grid-image_periods=1.334_d47dd95c.png' \n",
+      "periods=1.778 -> output_filename='2024-07-14_caustique/caustique_grid-image_periods=1.778_69b38a9d.png' \n",
+      "periods=2.371 -> output_filename='2024-07-14_caustique/caustique_grid-image_periods=2.371_56d7fff7.png' \n",
+      "periods=3.162 -> output_filename='2024-07-14_caustique/caustique_grid-image_periods=3.162_625ad5df.png' \n",
+      "periods=4.217 -> output_filename='2024-07-14_caustique/caustique_grid-image_periods=4.217_4e0b51a7.png' \n",
+      "periods=5.623 -> output_filename='2024-07-14_caustique/caustique_grid-image_periods=5.623_7fd080aa.png' \n",
+      "periods=7.499 -> output_filename='2024-07-14_caustique/caustique_grid-image_periods=7.499_abf0d88a.png' \n",
+      "periods=10.000 -> output_filename='2024-07-14_caustique/caustique_grid-image_periods=10.000_62096666.png' \n"
+     ]
+    }
+   ],
+   "source": [
+    "for periods in np.logspace(0, 1, N_scan, base=10):\n",
+    "    opt = init()\n",
+    "    c = Caustique(opt)\n",
+    "\n",
+    "    c.opt.tag = f'{c.opt.tag}_{type}-image_{periods=:.3f}'\n",
+    "    image = generate_image(nx=c.opt.nx, ny=c.opt.ny, periods=periods, threshold=.2)\n",
+    "    output_filename = c.plot(z, image)\n",
+    "    print(f'{periods=:.3f} -> {output_filename=} ')\n",
+    "    if c.opt.do_display: c.show(output_filename)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "tags": []
+   },
+   "source": [
+    "## shining a hole image to the wave"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "type = 'hole'"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "def generate_image(nx, ny, periods=6.5, threshold=0.45, radius=.9):\n",
+    "    X, Y = np.meshgrid(np.linspace(-1, 1, nx, endpoint=True), np.linspace(-1, 1, ny, endpoint=True))\n",
+    "    image = (np.cos(2*np.pi*X*periods) > threshold)*1.\n",
+    "    image += (np.cos(2*np.pi*Y*periods) > threshold)*1.\n",
+    "    image = 1. - (image<=1)\n",
+    "    image *= (X**2 < radius**2) * (Y**2 < radius**2) * 1.\n",
+    "    return image\n",
+    "image = generate_image(nx=c.opt.nx, ny=c.opt.ny, periods=6.5, threshold=0.45, radius=.9)\n",
+    "plt.imshow(image, cmap='gray');"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<img src=\"2024-07-14_caustique/caustique_hole-image_9b4d2f3e.png\" width=\"1024\"/>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Image object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "c = Caustique(init())\n",
+    "c.opt.tag = f'{c.opt.tag}_{type}-image'\n",
+    "\n",
+    "output_filename = c.plot(z, image)\n",
+    "c.show(output_filename)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
+     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
+     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
+     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "H = 10.000 -> output_filename='2024-07-14_caustique/caustique_hole-image_H_10.000_ed7ca120.png' \n",
+      "H = 11.892 -> output_filename='2024-07-14_caustique/caustique_hole-image_H_11.892_ba2ac289.png' \n",
+      "H = 14.142 -> output_filename='2024-07-14_caustique/caustique_hole-image_H_14.142_a39fd2e5.png' \n",
+      "H = 16.818 -> output_filename='2024-07-14_caustique/caustique_hole-image_H_16.818_8b7fd1d1.png' \n",
+      "H = 20.000 -> output_filename='2024-07-14_caustique/caustique_hole-image_H_20.000_909186ef.png' \n",
+      "H = 23.784 -> output_filename='2024-07-14_caustique/caustique_hole-image_H_23.784_71395bee.png' \n",
+      "H = 28.284 -> output_filename='2024-07-14_caustique/caustique_hole-image_H_28.284_738e7644.png' \n",
+      "H = 33.636 -> output_filename='2024-07-14_caustique/caustique_hole-image_H_33.636_588d4492.png' \n",
+      "H = 40.000 -> output_filename='2024-07-14_caustique/caustique_hole-image_H_40.000_7e52add3.png' \n"
+     ]
+    }
+   ],
+   "source": [
+    "for H_ in c.opt.H*np.logspace(-1, 1, N_scan, base=base):\n",
+    "    opt = init()\n",
+    "    c = Caustique(opt)\n",
+    "    c.opt.H = H_\n",
+    "    c.opt.tag = f'{c.opt.tag}_{type}-image_H_{H_:.3f}'\n",
+    "    \n",
+    "    output_filename = c.plot(z, image)\n",
+    "    print(f'H = {H_:.3f} -> {output_filename=} ')\n",
+    "    if c.opt.do_display: c.show(output_filename)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
+     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
+     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
+     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "threshold=0.100 -> output_filename='2024-07-14_caustique/caustique_hole-image_threshold=0.100_e0d53e21.png' \n",
+      "threshold=0.200 -> output_filename='2024-07-14_caustique/caustique_hole-image_threshold=0.200_d43c8b6d.png' \n",
+      "threshold=0.300 -> output_filename='2024-07-14_caustique/caustique_hole-image_threshold=0.300_a4cc1983.png' \n",
+      "threshold=0.400 -> output_filename='2024-07-14_caustique/caustique_hole-image_threshold=0.400_37a4b140.png' \n",
+      "threshold=0.500 -> output_filename='2024-07-14_caustique/caustique_hole-image_threshold=0.500_e7001ca6.png' \n",
+      "threshold=0.600 -> output_filename='2024-07-14_caustique/caustique_hole-image_threshold=0.600_c46451fc.png' \n",
+      "threshold=0.700 -> output_filename='2024-07-14_caustique/caustique_hole-image_threshold=0.700_b9e5f689.png' \n",
+      "threshold=0.800 -> output_filename='2024-07-14_caustique/caustique_hole-image_threshold=0.800_8e55b3d4.png' \n",
+      "threshold=0.900 -> output_filename='2024-07-14_caustique/caustique_hole-image_threshold=0.900_ba85d5b7.png' \n"
+     ]
+    }
+   ],
+   "source": [
+    "for threshold in np.linspace(0, 1, N_scan+2, endpoint=True)[1:-1]:\n",
+    "    opt = init()\n",
+    "    c = Caustique(opt)\n",
+    "\n",
+    "    c.opt.tag = f'{c.opt.tag}_{type}-image_{threshold=:.3f}'\n",
+    "    image = generate_image(nx=c.opt.nx, ny=c.opt.ny, periods=6.5, threshold=threshold)\n",
+    "    output_filename = c.plot(z, image)\n",
+    "    print(f'{threshold=:.3f} -> {output_filename=} ')\n",
+    "    if c.opt.do_display: c.show(output_filename)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
+     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
+     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
+     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "periods=1.000 -> output_filename='2024-07-14_caustique/caustique_hole-image_periods=1.000_5d4213e7.png' \n",
+      "periods=1.334 -> output_filename='2024-07-14_caustique/caustique_hole-image_periods=1.334_5f014d84.png' \n",
+      "periods=1.778 -> output_filename='2024-07-14_caustique/caustique_hole-image_periods=1.778_bc297376.png' \n",
+      "periods=2.371 -> output_filename='2024-07-14_caustique/caustique_hole-image_periods=2.371_d4bb5cf6.png' \n",
+      "periods=3.162 -> output_filename='2024-07-14_caustique/caustique_hole-image_periods=3.162_8f04bd17.png' \n",
+      "periods=4.217 -> output_filename='2024-07-14_caustique/caustique_hole-image_periods=4.217_7cf8e0de.png' \n",
+      "periods=5.623 -> output_filename='2024-07-14_caustique/caustique_hole-image_periods=5.623_6c912984.png' \n",
+      "periods=7.499 -> output_filename='2024-07-14_caustique/caustique_hole-image_periods=7.499_08e4064f.png' \n",
+      "periods=10.000 -> output_filename='2024-07-14_caustique/caustique_hole-image_periods=10.000_da1a7415.png' \n"
+     ]
+    }
+   ],
+   "source": [
+    "for periods in np.logspace(0, 1, N_scan, base=10):\n",
+    "    opt = init()\n",
+    "    c = Caustique(opt)\n",
+    "\n",
+    "    c.opt.tag = f'{c.opt.tag}_{type}-image_{periods=:.3f}'\n",
+    "    image = generate_image(nx=c.opt.nx, ny=c.opt.ny, periods=periods, threshold=.2)\n",
+    "    output_filename = c.plot(z, image)\n",
+    "    print(f'{periods=:.3f} -> {output_filename=} ')\n",
+    "    if c.opt.do_display: c.show(output_filename)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "tags": []
+   },
+   "source": [
+    "## shining a square image to the wave"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "type = 'square'"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "def generate_image(nx, ny,  radius=.9):\n",
+    "    X, Y = np.meshgrid(np.linspace(-1, 1, nx, endpoint=True), np.linspace(-1, 1, ny, endpoint=True))\n",
+    "    image = (X**2 < radius**2) * (Y**2 < radius**2) * 1.\n",
+    "    return image\n",
+    "image = generate_image(nx=c.opt.nx, ny=c.opt.ny, radius=.9)\n",
+    "plt.imshow(image, cmap='gray');"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<img src=\"2024-07-14_caustique/caustique_square-image_831afd95.png\" width=\"1024\"/>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Image object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "c = Caustique(init())\n",
+    "c.opt.tag = f'{c.opt.tag}_{type}-image'\n",
+    "output_filename = c.plot(z, image)\n",
+    "c.show(output_filename)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
+     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
+     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
+     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "H = 10.000 -> output_filename='2024-07-14_caustique/caustique_square-image_H_10.000_29fdea66.png' \n",
+      "H = 11.892 -> output_filename='2024-07-14_caustique/caustique_square-image_H_11.892_f877ae42.png' \n",
+      "H = 14.142 -> output_filename='2024-07-14_caustique/caustique_square-image_H_14.142_c236fda9.png' \n",
+      "H = 16.818 -> output_filename='2024-07-14_caustique/caustique_square-image_H_16.818_5ded8ca9.png' \n",
+      "H = 20.000 -> output_filename='2024-07-14_caustique/caustique_square-image_H_20.000_463674a3.png' \n",
+      "H = 23.784 -> output_filename='2024-07-14_caustique/caustique_square-image_H_23.784_bf2d15b7.png' \n",
+      "H = 28.284 -> output_filename='2024-07-14_caustique/caustique_square-image_H_28.284_a4674159.png' \n",
+      "H = 33.636 -> output_filename='2024-07-14_caustique/caustique_square-image_H_33.636_d9a7af9e.png' \n",
+      "H = 40.000 -> output_filename='2024-07-14_caustique/caustique_square-image_H_40.000_a1234263.png' \n"
+     ]
+    }
+   ],
+   "source": [
+    "for H_ in c.opt.H*np.logspace(-1, 1, N_scan, base=base):\n",
+    "    opt = init()\n",
+    "    c = Caustique(opt)\n",
+    "    c.opt.H = H_\n",
+    "    c.opt.tag = f'{c.opt.tag}_{type}-image_H_{H_:.3f}'\n",
+    "    \n",
+    "    output_filename = c.plot(z, image)\n",
+    "    print(f'H = {H_:.3f} -> {output_filename=} ')\n",
+    "    if c.opt.do_display: c.show(output_filename)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
+     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
+     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
+     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "radius=0.111 -> output_filename='2024-07-14_caustique/caustique_square-image_radius=0.111_00468503.png' \n",
+      "radius=0.222 -> output_filename='2024-07-14_caustique/caustique_square-image_radius=0.222_39ff64df.png' \n",
+      "radius=0.333 -> output_filename='2024-07-14_caustique/caustique_square-image_radius=0.333_8b81f3d3.png' \n",
+      "radius=0.444 -> output_filename='2024-07-14_caustique/caustique_square-image_radius=0.444_931bdf60.png' \n",
+      "radius=0.556 -> output_filename='2024-07-14_caustique/caustique_square-image_radius=0.556_e7c4815c.png' \n",
+      "radius=0.667 -> output_filename='2024-07-14_caustique/caustique_square-image_radius=0.667_aad700a5.png' \n",
+      "radius=0.778 -> output_filename='2024-07-14_caustique/caustique_square-image_radius=0.778_d61a88b5.png' \n",
+      "radius=0.889 -> output_filename='2024-07-14_caustique/caustique_square-image_radius=0.889_d328da03.png' \n",
+      "radius=1.000 -> output_filename='2024-07-14_caustique/caustique_square-image_radius=1.000_e8508b3d.png' \n"
+     ]
+    }
+   ],
+   "source": [
+    "for radius in np.linspace(0, 1, N_scan+1)[1:]:\n",
+    "    opt = init()\n",
+    "    c = Caustique(opt)\n",
+    "\n",
+    "    c.opt.tag = f'{c.opt.tag}_{type}-image_{radius=:.3f}'\n",
+    "    image = generate_image(nx=c.opt.nx, ny=c.opt.ny, radius=radius)\n",
+    "    output_filename = c.plot(z, image)\n",
+    "    print(f'{radius=:.3f} -> {output_filename=} ')\n",
+    "    if c.opt.do_display: c.show(output_filename)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "tags": []
+   },
+   "source": [
+    "## shining a disk image to the wave"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "type = 'disk'"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "def generate_image(nx, ny, radius_in=0., radius_out=.9):\n",
+    "    X, Y = np.meshgrid(np.linspace(-1, 1, nx, endpoint=True), np.linspace(-1, 1, ny, endpoint=True))\n",
+    "    image = ((X**2 + Y**2) < radius_out**2) * ((X**2 + Y**2) > radius_in**2) * 1.\n",
+    "    return image\n",
+    "image = generate_image(nx=c.opt.nx, ny=c.opt.ny, radius_out=.9)\n",
+    "plt.imshow(image, cmap='gray');"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<img src=\"2024-07-14_caustique/caustique_disk-image_b7bfbb25.png\" width=\"1024\"/>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Image object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "c = Caustique(init())\n",
+    "c.opt.tag = f'{c.opt.tag}_{type}-image'\n",
+    "output_filename = c.plot(z, image)\n",
+    "c.show(output_filename)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
+     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
+     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
+     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "H = 10.000 -> output_filename='2024-07-14_caustique/caustique_disk-image_H_10.000_e9ee9daa.png' \n",
+      "H = 11.892 -> output_filename='2024-07-14_caustique/caustique_disk-image_H_11.892_7f157ba1.png' \n",
+      "H = 14.142 -> output_filename='2024-07-14_caustique/caustique_disk-image_H_14.142_6b8bc48c.png' \n",
+      "H = 16.818 -> output_filename='2024-07-14_caustique/caustique_disk-image_H_16.818_68d5f977.png' \n",
+      "H = 20.000 -> output_filename='2024-07-14_caustique/caustique_disk-image_H_20.000_8c8148a7.png' \n",
+      "H = 23.784 -> output_filename='2024-07-14_caustique/caustique_disk-image_H_23.784_a8b0ecba.png' \n",
+      "H = 28.284 -> output_filename='2024-07-14_caustique/caustique_disk-image_H_28.284_82d58723.png' \n",
+      "H = 33.636 -> output_filename='2024-07-14_caustique/caustique_disk-image_H_33.636_a39ed8eb.png' \n",
+      "H = 40.000 -> output_filename='2024-07-14_caustique/caustique_disk-image_H_40.000_5cd93cdb.png' \n"
+     ]
+    }
+   ],
+   "source": [
+    "for H_ in c.opt.H*np.logspace(-1, 1, N_scan, base=base):\n",
+    "    opt = init()\n",
+    "    c = Caustique(opt)\n",
+    "    c.opt.H = H_\n",
+    "    c.opt.tag = f'{c.opt.tag}_{type}-image_H_{H_:.3f}'\n",
+    "    \n",
+    "    output_filename = c.plot(z, image)\n",
+    "    print(f'H = {H_:.3f} -> {output_filename=} ')\n",
+    "    if c.opt.do_display: c.show(output_filename)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
+     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
+     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
+     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.111 -> output_filename='2024-07-14_caustique/caustique_disk-image_radius_out=0.111_f3fc86c5.png' \n",
+      "0.222 -> output_filename='2024-07-14_caustique/caustique_disk-image_radius_out=0.222_3a288309.png' \n",
+      "0.333 -> output_filename='2024-07-14_caustique/caustique_disk-image_radius_out=0.333_9ffb2eba.png' \n",
+      "0.444 -> output_filename='2024-07-14_caustique/caustique_disk-image_radius_out=0.444_577b8bbc.png' \n",
+      "0.556 -> output_filename='2024-07-14_caustique/caustique_disk-image_radius_out=0.556_e0573034.png' \n",
+      "0.667 -> output_filename='2024-07-14_caustique/caustique_disk-image_radius_out=0.667_ea0f63d0.png' \n",
+      "0.778 -> output_filename='2024-07-14_caustique/caustique_disk-image_radius_out=0.778_d52eb8d7.png' \n",
+      "0.889 -> output_filename='2024-07-14_caustique/caustique_disk-image_radius_out=0.889_3d0086d5.png' \n",
+      "1.000 -> output_filename='2024-07-14_caustique/caustique_disk-image_radius_out=1.000_5b486f33.png' \n"
+     ]
+    }
+   ],
+   "source": [
+    "for radius_out in np.linspace(0, 1, N_scan+1)[1:]:\n",
+    "    opt = init()\n",
+    "    c = Caustique(opt)\n",
+    "\n",
+    "    c.opt.tag = f'{c.opt.tag}_{type}-image_{radius_out=:.3f}'\n",
+    "    image = generate_image(nx=c.opt.nx, ny=c.opt.ny, radius_out=radius_out)\n",
+    "    output_filename = c.plot(z, image)\n",
+    "    print(f'{radius_out:.3f} -> {output_filename=} ')\n",
+    "    if c.opt.do_display: c.show(output_filename)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
+     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
+     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
+     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:21<00:00,  3.23s/it]\n",
+      "100%|██████████| 1/1 [04:21<00:00, 261.82s/it]\n",
+      "100%|██████████| 1/1 [00:17<00:00, 17.62s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "radius_in=0.111 -> output_filename='2024-07-14_caustique/caustique_disk-image_radius_in=0.111_a52cafcd.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:20<00:00,  3.22s/it]\n",
+      "100%|██████████| 1/1 [04:20<00:00, 260.61s/it]\n",
+      "100%|██████████| 1/1 [00:16<00:00, 16.73s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "radius_in=0.222 -> output_filename='2024-07-14_caustique/caustique_disk-image_radius_in=0.222_68cc1071.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:16<00:00,  3.16s/it]\n",
+      "100%|██████████| 1/1 [04:16<00:00, 256.03s/it]\n",
+      "100%|██████████| 1/1 [00:15<00:00, 15.34s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "radius_in=0.333 -> output_filename='2024-07-14_caustique/caustique_disk-image_radius_in=0.333_2a4bcf45.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:14<00:00,  3.14s/it]\n",
+      "100%|██████████| 1/1 [04:14<00:00, 254.15s/it]\n",
+      "100%|██████████| 1/1 [00:13<00:00, 13.73s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "radius_in=0.444 -> output_filename='2024-07-14_caustique/caustique_disk-image_radius_in=0.444_98903950.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:17<00:00,  3.18s/it]\n",
+      "100%|██████████| 1/1 [04:17<00:00, 257.65s/it]\n",
+      "100%|██████████| 1/1 [00:12<00:00, 12.01s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "radius_in=0.556 -> output_filename='2024-07-14_caustique/caustique_disk-image_radius_in=0.556_06f94a7c.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:13<00:00,  3.13s/it]\n",
+      "100%|██████████| 1/1 [04:13<00:00, 253.80s/it]\n",
+      "100%|██████████| 1/1 [00:09<00:00,  9.89s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "radius_in=0.667 -> output_filename='2024-07-14_caustique/caustique_disk-image_radius_in=0.667_9b413d52.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:13<00:00,  3.12s/it]\n",
+      "100%|██████████| 1/1 [04:13<00:00, 253.02s/it]\n",
+      "100%|██████████| 1/1 [00:07<00:00,  7.71s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "radius_in=0.778 -> output_filename='2024-07-14_caustique/caustique_disk-image_radius_in=0.778_6e4b7d17.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:12<00:00,  3.11s/it]\n",
+      "100%|██████████| 1/1 [04:12<00:00, 252.28s/it]\n",
+      "100%|██████████| 1/1 [00:05<00:00,  5.62s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "radius_in=0.889 -> output_filename='2024-07-14_caustique/caustique_disk-image_radius_in=0.889_5976355d.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "  0%|          | 0/1 [00:00<?, ?it/s]/Users/laurentperrinet/app54_nextcloud/NaturalPatterns/2020_caustiques/.venv/lib/python3.12/site-packages/numpy/lib/_histograms_impl.py:1077: RuntimeWarning: invalid value encountered in divide\n",
+      "  hist /= s\n",
+      "100%|██████████| 81/81 [04:13<00:00,  3.13s/it]\n",
+      "100%|██████████| 1/1 [04:13<00:00, 253.86s/it]\n",
+      "100%|██████████| 1/1 [00:07<00:00,  7.14s/it]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "radius_in=1.000 -> output_filename='2024-07-14_caustique/caustique_disk-image_radius_in=1.000_ad622c1a.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "for radius_in in np.linspace(0, 1, N_scan+1)[1:]:\n",
+    "    opt = init()\n",
+    "    c = Caustique(opt)\n",
+    "\n",
+    "    c.opt.tag = f'{c.opt.tag}_{type}-image_{radius_in=:.3f}'\n",
+    "    image = generate_image(nx=c.opt.nx, ny=c.opt.ny, radius_in=radius_in)\n",
+    "    output_filename = c.plot(z, image)\n",
+    "    print(f'{radius_in=:.3f} -> {output_filename=} ')\n",
+    "    if c.opt.do_display: c.show(output_filename)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "tags": []
+   },
+   "source": [
+    "## shining a bi-grating image to the wave"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "def generate_image(nx, ny, period1=2, period2=64, threshold=0.3, radius=.9):\n",
+    "    X, Y = np.meshgrid(np.linspace(-1, 1, nx, endpoint=True), np.linspace(-1, 1, ny, endpoint=True))\n",
+    "    image  = (np.cos(2*np.pi*X*period1) > threshold) * 1.\n",
+    "    image *= np.cos(2*np.pi*X*period2) > threshold\n",
+    "    image *= (X**2 < radius**2) * (Y**2 < radius**2)\n",
+    "    return image\n",
+    "image = generate_image(nx=c.opt.nx, ny=c.opt.ny)\n",
+    "plt.imshow(image, cmap='gray');"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:12<00:00,  3.12s/it]\n",
+      "100%|██████████| 1/1 [04:12<00:00, 252.94s/it]\n",
+      "100%|██████████| 1/1 [00:07<00:00,  7.83s/it]\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "<img src=\"2024-07-14_caustique/caustique_bigrating-image_7334fb90.png\" width=\"1024\"/>"
+      ],
+      "text/plain": [
+       "<IPython.core.display.Image object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "type = 'bigrating'\n",
+    "c = Caustique(init())\n",
+    "c.opt.tag = f'{c.opt.tag}_{type}-image'\n",
+    "output_filename = c.plot(z, image)\n",
+    "c.show(output_filename)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
+     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
+     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
+     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:07<00:00,  3.05s/it]\n",
+      "100%|██████████| 1/1 [04:07<00:00, 247.03s/it]\n",
+      "100%|██████████| 1/1 [00:07<00:00,  7.01s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "H = 10.000 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_H_10.000_076e8456.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:08<00:00,  3.07s/it]\n",
+      "100%|██████████| 1/1 [04:08<00:00, 248.34s/it]\n",
+      "100%|██████████| 1/1 [00:07<00:00,  7.03s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "H = 11.892 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_H_11.892_12a2c5a2.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:10<00:00,  3.09s/it]\n",
+      "100%|██████████| 1/1 [04:10<00:00, 250.54s/it]\n",
+      "100%|██████████| 1/1 [00:07<00:00,  7.22s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "H = 14.142 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_H_14.142_767eb97e.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:12<00:00,  3.11s/it]\n",
+      "100%|██████████| 1/1 [04:12<00:00, 252.10s/it]\n",
+      "100%|██████████| 1/1 [00:07<00:00,  7.55s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "H = 16.818 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_H_16.818_6e17385b.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:14<00:00,  3.15s/it]\n",
+      "100%|██████████| 1/1 [04:14<00:00, 254.96s/it]\n",
+      "100%|██████████| 1/1 [00:07<00:00,  7.81s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "H = 20.000 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_H_20.000_cd36df60.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:16<00:00,  3.16s/it]\n",
+      "100%|██████████| 1/1 [04:16<00:00, 256.14s/it]\n",
+      "100%|██████████| 1/1 [00:08<00:00,  8.26s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "H = 23.784 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_H_23.784_ee16fadd.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:19<00:00,  3.20s/it]\n",
+      "100%|██████████| 1/1 [04:19<00:00, 259.42s/it]\n",
+      "100%|██████████| 1/1 [00:08<00:00,  8.91s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "H = 28.284 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_H_28.284_4b6d6a80.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:23<00:00,  3.25s/it]\n",
+      "100%|██████████| 1/1 [04:23<00:00, 263.20s/it]\n",
+      "100%|██████████| 1/1 [00:10<00:00, 10.47s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "H = 33.636 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_H_33.636_5be293cb.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:25<00:00,  3.28s/it]\n",
+      "100%|██████████| 1/1 [04:25<00:00, 265.49s/it]\n",
+      "100%|██████████| 1/1 [00:11<00:00, 11.02s/it]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "H = 40.000 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_H_40.000_6b678795.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "for H_ in c.opt.H*np.logspace(-1, 1, N_scan, base=base):\n",
+    "    opt = init()\n",
+    "    c = Caustique(opt)\n",
+    "    c.opt.H = H_\n",
+    "    c.opt.tag = f'{c.opt.tag}_{type}-image_H_{H_:.3f}'\n",
+    "    \n",
+    "    output_filename = c.plot(z, image)\n",
+    "    print(f'H = {H_:.3f} -> {output_filename=} ')\n",
+    "    if c.opt.do_display: c.show(output_filename)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
+     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
+     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
+     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:13<00:00,  3.13s/it]\n",
+      "100%|██████████| 1/1 [04:13<00:00, 253.79s/it]\n",
+      "100%|██████████| 1/1 [00:08<00:00,  8.99s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.100 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_threshold=0.100_167f88e3.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:14<00:00,  3.14s/it]\n",
+      "100%|██████████| 1/1 [04:14<00:00, 254.33s/it]\n",
+      "100%|██████████| 1/1 [00:08<00:00,  8.52s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.200 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_threshold=0.200_c7d579d7.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:14<00:00,  3.14s/it]\n",
+      "100%|██████████| 1/1 [04:14<00:00, 254.12s/it]\n",
+      "100%|██████████| 1/1 [00:08<00:00,  8.10s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.300 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_threshold=0.300_bd10d43b.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:14<00:00,  3.14s/it]\n",
+      "100%|██████████| 1/1 [04:14<00:00, 254.07s/it]\n",
+      "100%|██████████| 1/1 [00:07<00:00,  7.76s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.400 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_threshold=0.400_fea69475.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:13<00:00,  3.13s/it]\n",
+      "100%|██████████| 1/1 [04:13<00:00, 253.93s/it]\n",
+      "100%|██████████| 1/1 [00:07<00:00,  7.36s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.500 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_threshold=0.500_cd7b7266.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:13<00:00,  3.13s/it]\n",
+      "100%|██████████| 1/1 [04:13<00:00, 253.80s/it]\n",
+      "100%|██████████| 1/1 [00:06<00:00,  6.80s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.600 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_threshold=0.600_9df3f930.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:14<00:00,  3.14s/it]\n",
+      "100%|██████████| 1/1 [04:14<00:00, 254.50s/it]\n",
+      "100%|██████████| 1/1 [00:06<00:00,  6.68s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.700 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_threshold=0.700_eec2a7f5.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:14<00:00,  3.14s/it]\n",
+      "100%|██████████| 1/1 [04:14<00:00, 254.74s/it]\n",
+      "100%|██████████| 1/1 [00:06<00:00,  6.26s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.800 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_threshold=0.800_91875793.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:14<00:00,  3.14s/it]\n",
+      "100%|██████████| 1/1 [04:14<00:00, 254.12s/it]\n",
+      "100%|██████████| 1/1 [00:06<00:00,  6.03s/it]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.900 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_threshold=0.900_e21bf350.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "for threshold in np.linspace(0, 1, N_scan+2, endpoint=True)[1:-1]:\n",
+    "    opt = init()\n",
+    "    c = Caustique(opt)\n",
+    "\n",
+    "    c.opt.tag = f'{c.opt.tag}_{type}-image_{threshold=:.3f}'\n",
+    "    image = generate_image(nx=c.opt.nx, ny=c.opt.ny, threshold=threshold)\n",
+    "    output_filename = c.plot(z, image)\n",
+    "    print(f'{threshold:.3f} -> {output_filename=} ')\n",
+    "    if c.opt.do_display: c.show(output_filename)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
+     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
+     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
+     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:14<00:00,  3.14s/it]\n",
+      "100%|██████████| 1/1 [04:14<00:00, 254.21s/it]\n",
+      "100%|██████████| 1/1 [00:06<00:00,  6.00s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "radius=0.111 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_radius=0.111_99e32cee.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:14<00:00,  3.14s/it]\n",
+      "100%|██████████| 1/1 [04:14<00:00, 254.48s/it]\n",
+      "100%|██████████| 1/1 [00:04<00:00,  4.99s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "radius=0.222 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_radius=0.222_5688a186.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:14<00:00,  3.14s/it]\n",
+      "100%|██████████| 1/1 [04:14<00:00, 254.28s/it]\n",
+      "100%|██████████| 1/1 [00:05<00:00,  5.11s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "radius=0.333 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_radius=0.333_9d950461.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:15<00:00,  3.15s/it]\n",
+      "100%|██████████| 1/1 [04:15<00:00, 255.05s/it]\n",
+      "100%|██████████| 1/1 [00:05<00:00,  5.47s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "radius=0.444 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_radius=0.444_b92706f3.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:16<00:00,  3.17s/it]\n",
+      "100%|██████████| 1/1 [04:16<00:00, 256.83s/it]\n",
+      "100%|██████████| 1/1 [00:06<00:00,  6.25s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "radius=0.556 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_radius=0.556_024efde4.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:13<00:00,  3.13s/it]\n",
+      "100%|██████████| 1/1 [04:13<00:00, 253.64s/it]\n",
+      "100%|██████████| 1/1 [00:07<00:00,  7.07s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "radius=0.667 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_radius=0.667_a8a32aba.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:13<00:00,  3.13s/it]\n",
+      "100%|██████████| 1/1 [04:13<00:00, 253.78s/it]\n",
+      "100%|██████████| 1/1 [00:07<00:00,  7.34s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "radius=0.778 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_radius=0.778_b6c14af2.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:13<00:00,  3.13s/it]\n",
+      "100%|██████████| 1/1 [04:13<00:00, 253.70s/it]\n",
+      "100%|██████████| 1/1 [00:07<00:00,  7.70s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "radius=0.889 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_radius=0.889_2aae3977.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:13<00:00,  3.13s/it]\n",
+      "100%|██████████| 1/1 [04:13<00:00, 253.63s/it]\n",
+      "100%|██████████| 1/1 [00:10<00:00, 10.09s/it]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "radius=1.000 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_radius=1.000_e70339cb.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "for radius in np.linspace(0, 1, N_scan+1)[1:]:\n",
+    "    opt = init()\n",
+    "    c = Caustique(opt)\n",
+    "\n",
+    "    c.opt.tag = f'{c.opt.tag}_{type}-image_{radius=:.3f}'\n",
+    "    image = generate_image(nx=c.opt.nx, ny=c.opt.ny, radius=radius)\n",
+    "    output_filename = c.plot(z, image)\n",
+    "    print(f'{radius=:.3f} -> {output_filename=} ')\n",
+    "    if c.opt.do_display: c.show(output_filename)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
+     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
+     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
+     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:13<00:00,  3.13s/it]\n",
+      "100%|██████████| 1/1 [04:13<00:00, 253.81s/it]\n",
+      "100%|██████████| 1/1 [00:07<00:00,  7.68s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "period1=1.000 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_period1=1.00e+00_ec1598a7.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:14<00:00,  3.14s/it]\n",
+      "100%|██████████| 1/1 [04:14<00:00, 254.05s/it]\n",
+      "100%|██████████| 1/1 [00:09<00:00,  9.07s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "period1=1.334 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_period1=1.33e+00_9ec29307.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:14<00:00,  3.14s/it]\n",
+      "100%|██████████| 1/1 [04:14<00:00, 254.50s/it]\n",
+      "100%|██████████| 1/1 [00:08<00:00,  8.09s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "period1=1.778 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_period1=1.78e+00_482be7c6.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:14<00:00,  3.14s/it]\n",
+      "100%|██████████| 1/1 [04:14<00:00, 254.12s/it]\n",
+      "100%|██████████| 1/1 [00:09<00:00,  9.12s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "period1=2.371 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_period1=2.37e+00_1e189200.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:13<00:00,  3.13s/it]\n",
+      "100%|██████████| 1/1 [04:13<00:00, 253.65s/it]\n",
+      "100%|██████████| 1/1 [00:08<00:00,  8.74s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "period1=3.162 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_period1=3.16e+00_dc9e633c.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:14<00:00,  3.14s/it]\n",
+      "100%|██████████| 1/1 [04:14<00:00, 254.18s/it]\n",
+      "100%|██████████| 1/1 [00:08<00:00,  8.94s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "period1=4.217 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_period1=4.22e+00_557e6d53.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:13<00:00,  3.13s/it]\n",
+      "100%|██████████| 1/1 [04:13<00:00, 253.79s/it]\n",
+      "100%|██████████| 1/1 [00:09<00:00,  9.57s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "period1=5.623 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_period1=5.62e+00_83515d48.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:14<00:00,  3.14s/it]\n",
+      "100%|██████████| 1/1 [04:14<00:00, 254.33s/it]\n",
+      "100%|██████████| 1/1 [00:09<00:00,  9.73s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "period1=7.499 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_period1=7.50e+00_7e92fdf5.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:15<00:00,  3.15s/it]\n",
+      "100%|██████████| 1/1 [04:15<00:00, 255.40s/it]\n",
+      "100%|██████████| 1/1 [00:10<00:00, 10.04s/it]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "period1=10.000 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_period1=1.00e+01_66b8c9aa.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "for period1 in np.logspace(0, 1, N_scan, base=10):\n",
+    "    opt = init()\n",
+    "    c = Caustique(opt)\n",
+    "\n",
+    "    c.opt.tag = f'{c.opt.tag}_{type}-image_{period1=:.2e}'\n",
+    "    image = generate_image(nx=c.opt.nx, ny=c.opt.ny, period1=period1)\n",
+    "    output_filename = c.plot(z, image)\n",
+    "    print(f'{period1=:.3f} -> {output_filename=} ')\n",
+    "    if c.opt.do_display: c.show(output_filename)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "execution": {
+     "iopub.execute_input": "2022-09-16T06:50:19.915420Z",
+     "iopub.status.busy": "2022-09-16T06:50:19.915215Z",
+     "iopub.status.idle": "2022-09-16T06:50:21.641723Z",
+     "shell.execute_reply": "2022-09-16T06:50:21.641154Z"
+    }
+   },
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:16<00:00,  3.16s/it]\n",
+      "100%|██████████| 1/1 [04:16<00:00, 256.15s/it]\n",
+      "100%|██████████| 1/1 [00:06<00:00,  6.39s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "period2=1.000 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_period2=1.000_2e0a614c.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:15<00:00,  3.15s/it]\n",
+      "100%|██████████| 1/1 [04:15<00:00, 255.47s/it]\n",
+      "100%|██████████| 1/1 [00:06<00:00,  6.52s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "period2=1.334 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_period2=1.334_5697e8a1.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:15<00:00,  3.16s/it]\n",
+      "100%|██████████| 1/1 [04:15<00:00, 255.72s/it]\n",
+      "100%|██████████| 1/1 [00:08<00:00,  8.60s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "period2=1.778 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_period2=1.778_2c81f4fc.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:15<00:00,  3.15s/it]\n",
+      "100%|██████████| 1/1 [04:15<00:00, 255.10s/it]\n",
+      "100%|██████████| 1/1 [00:07<00:00,  7.72s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "period2=2.371 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_period2=2.371_90348db7.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:13<00:00,  3.14s/it]\n",
+      "100%|██████████| 1/1 [04:13<00:00, 253.99s/it]\n",
+      "100%|██████████| 1/1 [00:06<00:00,  6.51s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "period2=3.162 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_period2=3.162_8f2b589c.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:13<00:00,  3.13s/it]\n",
+      "100%|██████████| 1/1 [04:13<00:00, 253.44s/it]\n",
+      "100%|██████████| 1/1 [00:07<00:00,  7.02s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "period2=4.217 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_period2=4.217_5a8339d1.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:14<00:00,  3.14s/it]\n",
+      "100%|██████████| 1/1 [04:14<00:00, 254.42s/it]\n",
+      "100%|██████████| 1/1 [00:07<00:00,  7.28s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "period2=5.623 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_period2=5.623_e2db9053.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:15<00:00,  3.15s/it]\n",
+      "100%|██████████| 1/1 [04:15<00:00, 255.01s/it]\n",
+      "100%|██████████| 1/1 [00:06<00:00,  6.78s/it]\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "period2=7.499 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_period2=7.499_a57e5d8b.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "100%|██████████| 81/81 [04:16<00:00,  3.17s/it]\n",
+      "100%|██████████| 1/1 [04:16<00:00, 256.56s/it]\n",
+      "100%|██████████| 1/1 [00:07<00:00,  7.58s/it]"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "period2=10.000 -> output_filename='2024-07-14_caustique/caustique_bigrating-image_period2=10.000_77f9726d.png' \n"
+     ]
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "for period2 in np.logspace(0, 1, N_scan, base=10):\n",
+    "    opt = init()\n",
+    "    c = Caustique(opt)\n",
+    "\n",
+    "    c.opt.tag = f'{c.opt.tag}_{type}-image_{period2=:.3f}'\n",
+    "    image = generate_image(nx=c.opt.nx, ny=c.opt.ny, period2=period2)\n",
+    "    output_filename = c.plot(z, image)\n",
+    "    print(f'{period2=:.3f} -> {output_filename=} ')\n",
+    "    if c.opt.do_display: c.show(output_filename)"
+   ]
+  }
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diff --git a/README.md b/README.md
index 485707b..440d12d 100644
--- a/README.md
+++ b/README.md
@@ -1,15 +1,15 @@
 # caustiques (2020) / iridiscence (2022)
 
-* This repository https://github.com/NaturalPatterns/2020_caustiques presents 2 succesive projects
+* This repository https://github.com/NaturalPatterns/2020_caustiques presents 2 succesive projects 
   1. One where I developped a modelling of caustics produced by shallow water and which are detailed in https://laurentperrinet.github.io/sciblog/posts/2020-06-19-caustic-optics.html
   2. Another, where I build upon that work to decompose the spectrum of light into its different wavelength, producing *iridescent caustics*.
- * Rendering of the [full notebook](https://naturalpatterns.github.io/2020_caustiques/) in which I explore the role of different parameters in prouding the images.
+* Rendering of the [full notebook](https://naturalpatterns.github.io/2020_caustiques/) in which I explore the role of different parameters in prouding the images.
 
 ## caustiques (2020)
 
-[![DOI](https://zenodo.org/badge/273226625.svg)](https://zenodo.org/badge/latestdoi/273226625)
+![DOI](https://zenodo.org/badge/273226625.svg)
 
-Caustics ([wikipedia](https://en.wikipedia.org/wiki/Caustic_(optics))) are luminous patterns which are resulting from the superposition of smoothly deviated light rays. It is the heart-shaped pattern in your cup of coffee which is formed as the rays of from the sun are reflected on the cup's surface. It is also the wiggly patterns of light that you will see on the floor of a pool as the sun's light is *refracted* at the surface of the water. Here we will simulate this particular physical phenomenon. Simply because they are mesmerizingly beautiful, but also as it is of interest in visual neuroscience. Indeed, it speaks to how images are formed (more on this later), hence how the brain may understand images.
+Caustics ([wikipedia](https://en.wikipedia.org/wiki/Caustic_\(optics\))) are luminous patterns which are resulting from the superposition of smoothly deviated light rays. It is the heart-shaped pattern in your cup of coffee which is formed as the rays of from the sun are reflected on the cup's surface. It is also the wiggly patterns of light that you will see on the floor of a pool as the sun's light is *refracted* at the surface of the water. Here we will simulate this particular physical phenomenon. Simply because they are mesmerizingly beautiful, but also as it is of interest in visual neuroscience. Indeed, it speaks to how images are formed (more on this later), hence how the brain may understand images.
 
 In [this post](https://laurentperrinet.github.io/sciblog/posts/2020-06-19-caustic-optics.html), I have developed a simple formalism to generate such patterns, with the paradoxical result that it is *very* simple to code yet generates patterns with great complexity, such as:
 
@@ -23,16 +23,16 @@ This is joint work with artist [Etienne Rey](https://laurentperrinet.github.io/a
 
 ## iridiscence (2022)
 
-Upon further observation, one may discover that caustics exhibit some [iridescence](https://en.wikipedia.org/wiki/Iridescence)$^\ddagger$, that is, that the light pattern which forms the waggling lines of the caustics may decompose into different colors, forming evanescent rainbows. Here, we will simply use a modulation of the [Snell-Descartes law](https://en.wikipedia.org/wiki/Snell's_law) that we used to compute different angle of refraction. This will be put in relation with the dependance of the refraction index with the wavelength of light and the transformation of a [monochromatic light into RGB](https://github.com/laurentperrinet/lambda2color) that we used in a previous post about [colors of the sky](https://laurentperrinet.github.io/sciblog/posts/2020-07-04-colors-of-the-sky.html). The results are close to subjective observations, with the surprising (to me) observation that colors appear more *between* nodes...
-  
+Upon further observation, one may discover that caustics exhibit some [iridescence](https://en.wikipedia.org/wiki/Iridescence)$^\\ddagger$, that is, that the light pattern which forms the waggling lines of the caustics may decompose into different colors, forming evanescent rainbows. Here, we will simply use a modulation of the [Snell-Descartes law](https://en.wikipedia.org/wiki/Snell's_law) that we used to compute different angle of refraction. This will be put in relation with the dependance of the refraction index with the wavelength of light and the transformation of a [monochromatic light into RGB](https://github.com/laurentperrinet/lambda2color) that we used in a previous post about [colors of the sky](https://laurentperrinet.github.io/sciblog/posts/2020-07-04-colors-of-the-sky.html). The results are close to subjective observations, with the surprising (to me) observation that colors appear more *between* nodes...
+
 <BR>
 <center>
 <img src="iridiscence.mp4" width="100%"/>
 </center>
 <BR>
 
-Note: $\ddagger$ I use the term iridescence which is improper in the physical sense as it rather concerns the property of an object to exhibit different colors depending on the angle of view. However, in the perspective of the work with [Etienne Rey](https://laurentperrinet.github.io/authors/etienne-rey/) it resonates with our endeavour to show that percepetion, in particular visual perception, is an active process of the observer within its environment.
-  
+Note: $\\ddagger$ I use the term iridescence which is improper in the physical sense as it rather concerns the property of an object to exhibit different colors depending on the angle of view. However, in the perspective of the work with [Etienne Rey](https://laurentperrinet.github.io/authors/etienne-rey/) it resonates with our endeavour to show that percepetion, in particular visual perception, is an active process of the observer within its environment.
+
 ## installation
 
 Install [dependencies](https://pip.pypa.io/en/stable/user_guide/#requirements-files), then this library:
@@ -41,6 +41,7 @@ Install [dependencies](https://pip.pypa.io/en/stable/user_guide/#requirements-fi
 python3 -m pip install -r requirements.txt
 python3 -m pip install -e .
 ```
+
 ## running it
 
 ```
@@ -56,4 +57,4 @@ gifname = c.plot(z)
 
 ## exploring more
 
-Launch [jupyter](https://jupyter.org/) and open the notebook.
+Launch [jupyter](https://jupyter.org/) and open the notebook.
\ No newline at end of file