diff --git a/.gitignore b/.gitignore
deleted file mode 100644
index e69de29..0000000
diff --git a/chapters/Chapter 2 - Generative Models.ipynb b/chapters/Chapter 2 - Generative Models.ipynb
index 4406ac0..49cd023 100644
--- a/chapters/Chapter 2 - Generative Models.ipynb	
+++ b/chapters/Chapter 2 - Generative Models.ipynb	
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 112,
    "metadata": {
     "ExecuteTime": {
      "end_time": "2019-09-11T05:34:01.171283Z",
@@ -15,6 +15,7 @@
     "\n",
     "%matplotlib inline\n",
     "import matplotlib.pyplot as plt\n",
+    "from matplotlib.patches import Rectangle\n",
     "import numpy as np\n",
     "\n",
     "import pyro\n",
@@ -22,7 +23,21 @@
     "import torch\n",
     "\n",
     "import sys; sys.path.append('..')\n",
-    "from pyro_webppl import viz"
+    "from pyro_webppl import viz\n",
+    "\n",
+    "# imports for physics example:\n",
+    "from pyro_webppl.physics_example import Block, Simulate, Animate, infer_physics, draw_world, run_simulation\n",
+    "\n",
+    "import pyglet\n",
+    "from pyglet.gl import *\n",
+    "from pyglet.window import key, mouse\n",
+    "\n",
+    "import pymunk\n",
+    "import pymunk.pyglet_util\n",
+    "from pymunk import Vec2d\n",
+    "\n",
+    "from copy import deepcopy\n",
+    "from pyro.infer import Importance, EmpiricalMarginal"
    ]
   },
   {
@@ -233,15 +248,15 @@
      "output_type": "stream",
      "text": [
       "tensor(0.)\n",
-      "tensor(0.)\n",
-      "tensor(1.)\n",
-      "tensor(1.)\n",
       "tensor(1.)\n",
       "tensor(1.)\n",
+      "tensor(0.)\n",
       "tensor(1.)\n",
       "tensor(0.)\n",
+      "tensor(1.)\n",
       "tensor(0.)\n",
-      "tensor(0.)\n"
+      "tensor(1.)\n",
+      "tensor(1.)\n"
      ]
     }
    ],
@@ -272,14 +287,12 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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gV7x522nXHBHrgCeARzPz1zPzTLg/Rq/X+bbMvDQz3w/sAo5l5s53+LPWitOumdnf6uhExPa57Y8A/zTkGfut15q/C7w3fvj+x3Us8RbAa8mw+7Xqg1/x5m0N1vwLzL6nuycinpv778EWR16xhq/zGaXXmjPzNeCjwAMR8S/AzwCfbW/ilWuw5hPADcCjEfEC8AngxtYGHpC2+uXN0ySpiFV/hS9J6g+DL0lFGHxJKsLgS1IRBl+SijD4klSEwZekIgy+JBXxfxuYL7zXBFF1AAAAAElFTkSuQmCC\n",
+      "image/png": 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",
       "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
+       "<Figure size 640x480 with 1 Axes>"
       ]
      },
-     "metadata": {
-      "needs_background": "light"
-     },
+     "metadata": {},
      "output_type": "display_data"
     }
    ],
@@ -315,14 +328,14 @@
      "text": [
       "tensor(2.)\n",
       "tensor(2.)\n",
+      "tensor(0.)\n",
       "tensor(1.)\n",
       "tensor(1.)\n",
-      "tensor(0.)\n",
       "tensor(2.)\n",
       "tensor(2.)\n",
-      "tensor(2.)\n",
-      "tensor(2.)\n",
-      "tensor(1.)\n"
+      "tensor(3.)\n",
+      "tensor(0.)\n",
+      "tensor(2.)\n"
      ]
     }
    ],
@@ -353,14 +366,12 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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",
       "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
+       "<Figure size 640x480 with 1 Axes>"
       ]
      },
-     "metadata": {
-      "needs_background": "light"
-     },
+     "metadata": {},
      "output_type": "display_data"
     }
    ],
@@ -397,12 +408,12 @@
       "3\n",
       "3\n",
       "6\n",
-      "3\n",
-      "3\n",
-      "3\n",
+      "6\n",
+      "6\n",
       "3\n",
       "6\n",
-      "3\n"
+      "6\n",
+      "6\n"
      ]
     }
    ],
@@ -449,14 +460,12 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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",
       "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
+       "<Figure size 640x480 with 1 Axes>"
       ]
      },
-     "metadata": {
-      "needs_background": "light"
-     },
+     "metadata": {},
      "output_type": "display_data"
     }
    ],
@@ -484,14 +493,12 @@
    "outputs": [
     {
      "data": {
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",
       "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
+       "<Figure size 640x480 with 1 Axes>"
       ]
      },
-     "metadata": {
-      "needs_background": "light"
-     },
+     "metadata": {},
      "output_type": "display_data"
     }
    ],
@@ -519,38 +526,32 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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",
       "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
+       "<Figure size 640x480 with 1 Axes>"
       ]
      },
-     "metadata": {
-      "needs_background": "light"
-     },
+     "metadata": {},
      "output_type": "display_data"
     },
     {
      "data": {
-      "image/png": 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\n",
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",
       "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
+       "<Figure size 640x480 with 1 Axes>"
       ]
      },
-     "metadata": {
-      "needs_background": "light"
-     },
+     "metadata": {},
      "output_type": "display_data"
     },
     {
      "data": {
-      "image/png": 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\n",
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",
       "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
+       "<Figure size 640x480 with 1 Axes>"
       ]
      },
-     "metadata": {
-      "needs_background": "light"
-     },
+     "metadata": {},
      "output_type": "display_data"
     }
    ],
@@ -586,14 +587,12 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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",
       "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
+       "<Figure size 640x480 with 1 Axes>"
       ]
      },
-     "metadata": {
-      "needs_background": "light"
-     },
+     "metadata": {},
      "output_type": "display_data"
     }
    ],
@@ -633,14 +632,12 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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",
       "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
+       "<Figure size 640x480 with 1 Axes>"
       ]
      },
-     "metadata": {
-      "needs_background": "light"
-     },
+     "metadata": {},
      "output_type": "display_data"
     }
    ],
@@ -721,7 +718,7 @@
     {
      "data": {
       "text/plain": [
-       "{'cough': True,\n",
+       "{'cough': False,\n",
        " 'fever': False,\n",
        " 'chest_pain': False,\n",
        " 'shortness_of_breath': False}"
@@ -816,7 +813,7 @@
     {
      "data": {
       "text/plain": [
-       "[tensor(1.), tensor(0.)]"
+       "[tensor(0.), tensor(1.)]"
       ]
      },
      "execution_count": 16,
@@ -852,14 +849,12 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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\n",
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",
       "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
+       "<Figure size 640x480 with 1 Axes>"
       ]
      },
-     "metadata": {
-      "needs_background": "light"
-     },
+     "metadata": {},
      "output_type": "display_data"
     }
    ],
@@ -914,20 +909,18 @@
      "output_type": "stream",
      "text": [
       "type  <class 'pyro.distributions.torch.Bernoulli'>\n",
-      "sample  tensor(0.)\n",
+      "sample  tensor(1.)\n",
       "log prob  tensor(-0.6931)\n"
      ]
     },
     {
      "data": {
-      "image/png": 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vx4A3n+aYB2j9fOmbwBHg7zLzGwswa0m+eZokFeEVviQVYfAlqQiDL0lFGHxJKsLgS1IRBl+SijD4klSEwZekIv4P26IXnvDtK88AAAAASUVORK5CYII=\n",
+      "image/png": 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",
       "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
+       "<Figure size 640x480 with 1 Axes>"
       ]
      },
-     "metadata": {
-      "needs_background": "light"
-     },
+     "metadata": {},
      "output_type": "display_data"
     }
    ],
@@ -940,7 +933,7 @@
     "print('sample ', d.sample())\n",
     "\n",
     "# compute the log-probability of sampling true:\n",
-    "print('log prob ', d.log_prob(False))\n",
+    "print('log prob ', d.log_prob(torch.tensor(1.0)))\n",
     "\n",
     "# visualize the distribution:\n",
     "plt.xticks([0, 1], labels=['heads', 'tails'])\n",
@@ -975,8 +968,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "sample  tensor(-0.2089)\n",
-      "foo  tensor(0.7000)\n"
+      "sample  tensor(0.5483)\n",
+      "foo  tensor(-0.2826)\n"
      ]
     }
    ],
@@ -1045,19 +1038,17 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "[0.0893535315990448, 0.006774185691028833, 0.4481070935726166, -0.027167800813913345, -2.064568042755127]\n"
+      "[-0.6225902438163757, 0.005093753803521395, 2.4754393100738525, -0.2677018642425537, -0.009533843025565147]\n"
      ]
     },
     {
      "data": {
-      "image/png": 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\n",
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",
       "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
+       "<Figure size 640x480 with 1 Axes>"
       ]
      },
-     "metadata": {
-      "needs_background": "light"
-     },
+     "metadata": {},
      "output_type": "display_data"
     }
    ],
@@ -1135,7 +1126,7 @@
     {
      "data": {
       "text/plain": [
-       "[tensor(0.), tensor(0.)]"
+       "[tensor(0.), tensor(1.)]"
       ]
      },
      "execution_count": 22,
@@ -1175,7 +1166,7 @@
     {
      "data": {
       "text/plain": [
-       "[tensor(1.), tensor(0.)]"
+       "[tensor(0.), tensor(1.)]"
       ]
      },
      "execution_count": 23,
@@ -1233,7 +1224,7 @@
     {
      "data": {
       "text/plain": [
-       "tensor(0.)"
+       "tensor(1.)"
       ]
      },
      "execution_count": 24,
@@ -1268,7 +1259,7 @@
     {
      "data": {
       "text/plain": [
-       "0.754"
+       "0.747"
       ]
      },
      "execution_count": 25,
@@ -1335,7 +1326,7 @@
     {
      "data": {
       "text/plain": [
-       "<BarContainer object of 7 artists>"
+       "<BarContainer object of 8 artists>"
       ]
      },
      "execution_count": 26,
@@ -1344,14 +1335,12 @@
     },
     {
      "data": {
-      "image/png": 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\n",
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",
       "text/plain": [
-       "<Figure size 432x288 with 1 Axes>"
+       "<Figure size 640x480 with 1 Axes>"
       ]
      },
-     "metadata": {
-      "needs_background": "light"
-     },
+     "metadata": {},
      "output_type": "display_data"
     }
    ],
@@ -1422,9 +1411,9 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "bob green\n",
-      "alice blue\n",
-      "bob brown\n"
+      "bob blue\n",
+      "alice brown\n",
+      "bob green\n"
      ]
     }
    ],
@@ -1470,16 +1459,16 @@
     {
      "data": {
       "text/plain": [
-       "[tensor(8),\n",
-       " tensor(7),\n",
-       " tensor(9),\n",
-       " tensor(9),\n",
+       "[tensor(2),\n",
+       " tensor(1),\n",
+       " tensor(8),\n",
        " tensor(5),\n",
+       " tensor(9),\n",
+       " tensor(6),\n",
        " tensor(0),\n",
-       " tensor(1),\n",
        " tensor(8),\n",
        " tensor(1),\n",
-       " tensor(4)]"
+       " tensor(2)]"
       ]
      },
      "execution_count": 29,
@@ -1514,16 +1503,16 @@
     {
      "data": {
       "text/plain": [
-       "[tensor(3),\n",
-       " tensor(3),\n",
-       " tensor(3),\n",
-       " tensor(3),\n",
-       " tensor(3),\n",
-       " tensor(3),\n",
-       " tensor(3),\n",
-       " tensor(3),\n",
-       " tensor(3),\n",
-       " tensor(3)]"
+       "[tensor(8),\n",
+       " tensor(8),\n",
+       " tensor(8),\n",
+       " tensor(8),\n",
+       " tensor(8),\n",
+       " tensor(8),\n",
+       " tensor(8),\n",
+       " tensor(8),\n",
+       " tensor(8),\n",
+       " tensor(8)]"
       ]
      },
      "execution_count": 30,
@@ -1561,7 +1550,7 @@
      "output_type": "stream",
      "text": [
       "bob blue\n",
-      "alice green\n",
+      "alice brown\n",
       "bob blue\n"
      ]
     }
@@ -1602,8 +1591,8 @@
     {
      "data": {
       "text/plain": [
-       "[[tensor(1.), tensor(1.), tensor(0.), tensor(0.)],\n",
-       " [tensor(1.), tensor(1.), tensor(0.), tensor(0.)]]"
+       "[[tensor(0.), tensor(1.), tensor(1.), tensor(1.)],\n",
+       " [tensor(0.), tensor(1.), tensor(1.), tensor(1.)]]"
       ]
      },
      "execution_count": 32,
@@ -1635,104 +1624,238 @@
     "heading_collapsed": true
    },
    "source": [
-    "# Intuitive Physics Example   - TODO"
+    "# Intuitive Physics Example\n",
+    "Humans have a deep intuitive understanding of everyday physics — this allows us to make furniture, appreciate sculpture, and play baseball. How can we describe this intuitive physics? One approach is to posit that humans have a generative model that captures key aspects of real physics, though perhaps with approximations and noise. This mental physics simulator could for instance approximate Newtonian mechanics, allowing us to imagine the future state of a collection of (rigid) bodies. We have included such a 2-dimensional physics simulator using Python's `Pymunk` and `Pyglet` modules.\n",
+    "\n",
+    "Pymunk is a 2D physics library, which we use to simulate the setup and progression of our 'world' - in this case, a series of stacked blocks. We use Pyglet to handle the animation of the simulation. Here we define a class `Simulate` that takes a collection of physical objects and runs physics 'forward' by some amount of time. We also have the class `Animate`, which does the same, but gives us an animation to see what is happening). We can use these to imagine the outcome of various initial states, as in the Plinko machine example above.\n",
+    "\n",
+    "There are many judgements that you could make with such a physics simulator. [Hamrick et al. (2011)](https://cseweb.ucsd.edu/~gary/cs200/s11/hamrick-etal-cogsci2011.pdf) have explored human intuitions about the stability of block towers. \n",
+    "\n",
+    "Run the cell below to look at several different random block towers; try to judge first whether you think the tower is stable. You can press `R` on your keyboard to load a new tower, and `Esc` to exit the animation window. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 117,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "DIMS = {\n",
+    "    \"WORLD_WIDTH\": 400,\n",
+    "    \"WORLD_HEIGHT\": 600,\n",
+    "    \"FLOOR_HEIGHT\": 50,\n",
+    "}\n",
+    "\n",
+    "animation = Animate(dims=DIMS)\n",
+    "pyglet.app.run()"
    ]
   },
   {
+   "attachments": {},
    "cell_type": "markdown",
-   "metadata": {
-    "hidden": true
-   },
+   "metadata": {},
    "source": [
-    "```javascript\n",
-    "var listMin = function(xs) {\n",
-    "  if (xs.length == 1) {\n",
-    "    return xs[0]\n",
-    "  } else {\n",
-    "    return Math.min(xs[0], listMin(rest(xs)))\n",
-    "  }\n",
-    "}\n",
+    "You can also see a recording of what this looks like here:\n",
     "\n",
-    "var ground = {shape: 'rect', static: true, dims: [worldWidth, 10],\n",
-    "              x: worldWidth/2, y: worldHeight+6};\n",
+    "<img src=\"../img/tower_animations.gif\" width=\"300\">"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Were you often right? Were there some cases of ‘surprisingly stable’ towers? [Hamrick et al. (2011)](https://cseweb.ucsd.edu/~gary/cs200/s11/hamrick-etal-cogsci2011.pdf) account for these cases by positing that people are not entirely sure where the blocks are initially (perhaps due to noise in visual perception). Thus our intuitions of stability are really stability given noise (or the expected stability marginalizing over slightly different initial configurations). \n",
     "\n",
-    "var stableWorld = [\n",
-    "  ground,\n",
-    "  {shape: 'rect', static: false, dims: [60, 22], x: 175, y: 473},\n",
-    "  {shape: 'rect', static: false, dims: [50, 38], x: 159.97995044874122, y: 413},\n",
-    "  {shape: 'rect', static: false, dims: [40, 35], x: 166.91912737427202, y: 340},\n",
-    "  {shape: 'rect', static: false, dims: [30, 29], x: 177.26195677111082, y: 276},\n",
-    "  {shape: 'rect', static: false, dims: [11, 17], x: 168.51354470809122, y: 230}\n",
+    "Let us now define some sample worlds - a *stable world* that always remains standing, an *unstable world* that almost always falls over, and an *almost unstable world*, that is precariously balanced, so sometimes falls and sometimes stands."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 116,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 400x600 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "stable_world = [\n",
+    "    Block(90, 50, 200, 75),\n",
+    "    Block(70, 80, 200, 140),\n",
+    "    Block(100, 30, 200, 195),\n",
+    "    Block(60, 45, 200, 232.5),\n",
+    "    Block(40, 20, 200, 265),\n",
     "]\n",
     "\n",
-    "var almostUnstableWorld = [\n",
-    "  ground,\n",
-    "  {shape: 'rect', static: false, dims: [24, 22], x: 175, y: 473},\n",
-    "  {shape: 'rect', static: false, dims: [15, 38], x: 159.97995044874122, y: 413},\n",
-    "  {shape: 'rect', static: false, dims: [11, 35], x: 166.91912737427202, y: 340},\n",
-    "  {shape: 'rect', static: false, dims: [11, 29], x: 177.26195677111082, y: 276},\n",
-    "  {shape: 'rect', static: false, dims: [11, 17], x: 168.51354470809122, y: 230}\n",
+    "almost_unstable_world = [\n",
+    "    Block(90, 50, 200, 75),\n",
+    "    Block(50, 70, 210, 135),\n",
+    "    Block(40, 40, 190, 190),\n",
+    "    Block(20, 80, 185, 250),\n",
+    "    Block(80, 20, 195, 300),\n",
     "]\n",
     "\n",
-    "var unstableWorld = [\n",
-    "  ground,\n",
-    "  {shape: 'rect', static: false, dims: [60, 22], x: 175, y: 473},\n",
-    "  {shape: 'rect', static: false, dims: [50, 38], x: 90, y: 413},\n",
-    "  {shape: 'rect', static: false, dims: [40, 35], x: 140, y: 340},\n",
-    "  {shape: 'rect', static: false, dims: [10, 29], x: 177.26195677111082, y: 276},\n",
-    "  {shape: 'rect', static: false, dims: [50, 17], x: 140, y: 230}\n",
+    "unstable_world = [\n",
+    "    Block(90, 50, 200, 75),\n",
+    "    Block(50, 70, 210, 135),\n",
+    "    Block(40, 40, 220, 190),\n",
+    "    Block(20, 80, 230, 250),\n",
+    "    Block(80, 20, 245, 300),\n",
     "]\n",
     "\n",
-    "var doesTowerFall = function (initialW, finalW) {\n",
-    "  var highestY = function (w) { listMin(map(function(obj) { return obj.y }, w)) }\n",
-    "  var approxEqual = function (a, b) { Math.abs(a - b) < 1.0 }\n",
-    "  !approxEqual(highestY(initialW), highestY(finalW))\n",
-    "}\n",
+    "# Uncomment any worlds you would like to see plotted\n",
+    "# draw_world(stable_world, DIMS)\n",
+    "draw_world(almost_unstable_world, DIMS)\n",
+    "# draw_world(unstable_world, DIMS)\n"
+   ]
+  },
+  {
+   "attachments": {},
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "We can then use Pyro to realize our measure of stability:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 115,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Variables sampled by Pyro in our model: \n",
+      "['_INPUT', 'noise_width', 'Block_0_x', 'Block_1_x', 'Block_2_x', 'Block_3_x', 'Block_4_x', 'Stability', '_RETURN']\n"
+     ]
+    }
+   ],
+   "source": [
+    "def model(world, dims):\n",
+    "    s = run_simulation(world, dims)\n",
+    "    Stability = pyro.sample(\"Stability\", dist.Delta(torch.tensor(s, dtype=torch.float)))\n",
+    "    return Stability\n",
     "\n",
-    "var noisify = function (world) {\n",
-    "  var perturbX = function (obj) {\n",
-    "    var noiseWidth = 10\n",
-    "    obj.static ? obj : _.extend({}, obj, {x: uniform(obj.x - noiseWidth, obj.x + noiseWidth) })\n",
-    "  }\n",
-    "  map(perturbX, world)\n",
-    "}\n",
+    "# Uncomment whichever of the models you would like to test:\n",
+    "# our_model = lambda: model(stable_world, DIMS)\n",
+    "our_model = lambda: model(almost_unstable_world, DIMS)\n",
+    "# our_model = lambda: model(unstable_world, DIMS)\n",
     "\n",
-    "var run = function(world) {\n",
-    "  var initialWorld = noisify(world)\n",
-    "  var finalWorld = physics.run(1000, initialWorld)\n",
-    "  doesTowerFall(initialWorld, finalWorld)\n",
-    "}\n",
+    "sampled_vars = list(pyro.poutine.trace(our_model).get_trace().nodes.keys())\n",
+    "print(f\"Variables sampled by Pyro in our model: \", sampled_vars, sep='\\n')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 94,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "P(Stable = True | noise_width = 5.0) = 0.5839999914169312\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# See how the results vary with nw = 1.0, 5.0 and 10.0\n",
+    "nw = 5.0\n",
+    "emp_marginal = infer_physics(\n",
+    "    our_model, \n",
+    "    conditions={\"noise_width\": torch.tensor(nw)},\n",
+    "    sites = [\"Stability\"],\n",
+    "    num_samples=500\n",
+    ")\n",
+    "\n",
+    "outcome = torch.tensor([True], dtype=torch.float)\n",
     "\n",
-    "viz(\n",
-    "  Infer({method: 'forward', samples: 100},\n",
-    "        function() { run(stableWorld) }))\n",
-    "viz(\n",
-    "  Infer({method: 'forward', samples: 100},\n",
-    "        function() { run(almostUnstableWorld) }))\n",
-    "viz(\n",
-    "  Infer({method: 'forward', samples: 100},\n",
-    "        function() { run(unstableWorld) }))\n",
+    "log_prob = emp_marginal.log_prob(outcome)\n",
+    "p = np.exp(log_prob)\n",
+    "print(f\"P(Stable = True | noise_width = 5.0) = {p}\")\n",
     "\n",
-    "// uncomment any of these that you'd like to see for yourself\n",
-    "// physics.animate(1000, stableWorld)\n",
-    "// physics.animate(1000, almostUnstableWorld)\n",
-    "// physics.animate(1000, unstableWorld)\n",
-    "```"
+    "if p != 1.0:\n",
+    "    viz(emp_marginal, plot_args={\"tick_label\":[\"False\", \"True\"], \"width\":0.6}, title=f\"Probability that model is stable given noise_width={nw}\")\n",
+    "else:\n",
+    "    print(\"No plot as we have a single bar!\")"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": null,
-   "metadata": {
-    "hidden": true
-   },
-   "outputs": [],
-   "source": []
+   "execution_count": 119,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "P(noise_width=1.0 | stable = True) = 0.24354243278503418\n",
+      "P(noise_width=5.0 | stable = True) = 0.5867159366607666\n",
+      "P(noise_width=10.0 | stable = True) = 0.1697417050600052\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "emp_marginal = infer_physics(\n",
+    "    our_model,\n",
+    "    conditions = {\"Stability\": torch.tensor(1.0)},\n",
+    "    sites = [\"noise_width\"],\n",
+    "    num_samples=500\n",
+    ")\n",
+    "\n",
+    "noise_widths = [1.0, 5.0, 10.0]\n",
+    "for nw in noise_widths:\n",
+    "    outcome = torch.tensor([nw])\n",
+    "\n",
+    "    log_prob = emp_marginal.log_prob(outcome)\n",
+    "    p = np.exp(log_prob)\n",
+    "    print(f\"P(noise_width={nw} | stable = True) = {p}\")\n",
+    "    \n",
+    "tick_labels = [str(item) for item in noise_widths]\n",
+    "# tick_labels = None\n",
+    "viz(emp_marginal, plot_args={\"tick_label\":tick_labels, \"width\": 1}, title=\"Probabilities that noise_width is a particular value given the model was stable\")"
+   ]
+  },
+  {
+   "attachments": {},
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Within the Simulate class, a noise_width value is picked from the options [1.0, 5.0, 10.0] with respective probabilities of being chosen of [0.2, 0.6, 0.2]. The plot above shows given the model is stable, we have a stronger belief that the noise_width value selected is 1.0 or 5.0, rather than the larger noise value of 10.0."
+   ]
   }
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3",
+   "display_name": "Python 3.10.4 ('causal-ml')",
    "language": "python",
    "name": "python3"
   },
@@ -1746,7 +1869,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.1"
+   "version": "3.10.4"
   },
   "toc": {
    "base_numbering": 1,
@@ -1789,6 +1912,11 @@
     "_Feature"
    ],
    "window_display": false
+  },
+  "vscode": {
+   "interpreter": {
+    "hash": "0e642de13ed24eb1e8129cfad9323b43f1e482b6af82b8c19b9795c172c70e2a"
+   }
   }
  },
  "nbformat": 4,
diff --git a/img/tower_animations.gif b/img/tower_animations.gif
new file mode 100644
index 0000000..f5e5b2a
Binary files /dev/null and b/img/tower_animations.gif differ
diff --git a/pyro_webppl/physics_example.py b/pyro_webppl/physics_example.py
new file mode 100644
index 0000000..0da757d
--- /dev/null
+++ b/pyro_webppl/physics_example.py
@@ -0,0 +1,228 @@
+import matplotlib.pyplot as plt
+from matplotlib.patches import Rectangle
+import numpy as np
+
+import pyro
+import pyro.distributions as dist
+import torch
+
+import sys; sys.path.append('..')
+from pyro_webppl import viz
+
+# imports for physics example:
+import pyglet
+from pyglet.gl import *
+from pyglet.window import key, mouse
+
+import pymunk
+import pymunk.pyglet_util
+from pymunk import Vec2d
+
+from copy import deepcopy
+from pyro.infer import Importance, EmpiricalMarginal
+
+
+class Block:
+    def __init__(self, width=None, height=None, x=0, y=0, is_first=False, is_static=False):
+        self.w = width
+        self.h = height
+        self.x = x
+        self.y = y
+        self.is_first = is_first
+        self.is_static = is_static
+        
+        if not self.w:
+            self.w = np.random.randint(50, 100)
+        if not self.h:
+            self.h = np.random.randint(50, 100)
+
+class Simulate:
+    def __init__(self, world=None, num_blocks=5, dims={}):
+        self.world = world
+        self.num_blocks = num_blocks
+        self.dims = dims
+
+        vals = torch.tensor([1.0, 5.0, 10.0], dtype=torch.float)
+        log_probs = torch.log(torch.tensor([0.2, 0.6, 0.2], dtype=torch.float))
+        noise_width = pyro.sample("noise_width", dist.Empirical(samples=vals, log_weights=log_probs))
+        self.noise_width = float(noise_width.item())
+
+        # create the simulation world
+        self.create_world()
+        
+    def create_world(self):
+        # Create the simulation world
+
+        self.space = pymunk.Space()
+        self.space.gravity = Vec2d(0.0, -200.0)
+        self.space.sleep_time_threshold = 1
+
+        # add the floor - other walls/bounds could be added here
+        static_lines = [
+            pymunk.Segment(self.space.static_body, Vec2d(-self.dims["WORLD_WIDTH"], self.dims["FLOOR_HEIGHT"]), Vec2d(self.dims["WORLD_WIDTH"]*2, self.dims["FLOOR_HEIGHT"]), 1),
+        ]
+
+        for l in static_lines:
+            l.friction = 0.3
+        self.space.add(*static_lines)
+
+        # create the blocks
+        if not self.world:
+            prev_block = self.add_block(None)
+            for idx in range(1, self.num_blocks):
+                next_block = self.add_block(idx, prev_block=prev_block)
+                prev_block = next_block    
+
+        else:
+            for idx, item in enumerate(self.world):
+                self.add_block(idx, new_block=item)
+
+        return 1
+
+    def add_block(self, idx, prev_block=None, new_block=None):
+        # function for creating and positioning blocks
+
+        if new_block == None:
+            block = Block()
+            if prev_block == None:
+                block.is_first = True
+                block.x = int(self.dims["WORLD_WIDTH"]/2)
+                block.y = self.dims["FLOOR_HEIGHT"] + block.h/2
+
+            else:
+                block.x = np.random.randint(prev_block.x - prev_block.w/2, prev_block.x + prev_block.w/2)
+                block.y = prev_block.y + prev_block.h/2 + block.h/2
+
+        else:
+            block = deepcopy(new_block)
+            vals = torch.tensor(list(range(int(np.floor(block.x-self.noise_width/2)), int(np.ceil(block.x+self.noise_width/2))+1)), dtype=torch.float)
+            log_probs = torch.log(torch.ones(vals.size(), dtype=torch.float))
+            Block_x = pyro.sample("Block_{}_x".format(idx), dist.Empirical(samples=vals, log_weights=log_probs))
+            block.x = int(Block_x.item())
+
+
+        # pymunk box coords are at Centre of Mass !
+        mass = block.w*block.h/100
+        moment = pymunk.moment_for_box(mass, (block.w, block.h))
+        body = pymunk.Body(mass, moment)
+        body.position = Vec2d(block.x, block.y)
+        shape = pymunk.Poly.create_box(body, (block.w, block.h))
+        shape.friction = 0.3
+        shape.color = (np.random.randint(50,150), np.random.randint(50,150), np.random.randint(100,255), 255)
+        self.space.add(body, shape)
+        return block
+        
+    def update(self, dt):
+        # Here we use a very basic way to keep a set space.step dt.
+        # For a real game its probably best to do something more complicated.
+        step_dt = 1 / 250.0
+        x = 0
+        while x < dt:
+            x += step_dt
+            self.space.step(step_dt)
+
+class Animate(pyglet.window.Window):
+    # main class for animation
+
+    def __init__(self, world=None, num_blocks=5, dims={}):
+
+        self.world=world
+        self.num_blocks=num_blocks
+        self.dims=dims
+        
+        #set the window size
+        self.window = pyglet.window.Window.__init__(self, width=self.dims["WORLD_WIDTH"], height= self.dims["WORLD_HEIGHT"], vsync=False)
+        self.set_caption("2D Boxes")
+        
+        # sets how frequently self.update gets called once sim starts
+        pyglet.clock.schedule_interval(self.update, 1 / 60.0)
+        # display FPS
+        self.fps_display = pyglet.window.FPSDisplay(self)
+
+        # create the simulation world
+        self.simulation = Simulate(self.world, self.num_blocks, self.dims)
+        self.simulation.create_world()
+
+        # add draw options
+        self.draw_options = pymunk.pyglet_util.DrawOptions()
+        self.draw_options.flags = self.draw_options.DRAW_SHAPES
+
+        # add some text
+        self.label = pyglet.text.Label('Hit R to reset', font_name='Times New Roman', font_size=16, x=10, y=self.dims["WORLD_HEIGHT"]-25)
+
+    def update(self, dt):
+        self.simulation.update(dt)
+
+    def on_key_press(self, symbol, modifiers):
+        
+        if symbol == key.R:
+            self.clear()
+            self.simulation = Simulate(self.world, self.num_blocks, dims=self.dims)
+            self.simulation.create_world()
+
+        elif symbol == key.ESCAPE:
+            self.close()
+            pyglet.app.exit()
+            
+        elif symbol == pyglet.window.key.P:
+            pyglet.image.get_buffer_manager().get_color_buffer().save(
+                "box2d_vertical_stack.png"
+            )
+
+    def on_draw(self):
+        self.clear()
+        # self.fps_display.draw()
+        self.simulation.space.debug_draw(self.draw_options)
+        self.label.draw()
+
+def does_tower_fall(initial_w, final_w):
+    """
+    Compare the final state of a tower to its initial state and determine whether or not it stayed standing. 
+    """
+    # here we compare the intial and final world states and see whether the highest block is roughly in the same place
+    def highest_y(w):
+        return max([b.y for b in w])
+
+    def approx_equal(a, b):
+        return (abs(a - b) < 1)
+
+    return not approx_equal(highest_y(initial_w), highest_y(final_w))
+
+
+def run_simulation(world, dims):
+    """
+    Run one iteration of a physics simulation for a given world. Returns the outcome of whether or not the tower was stable.
+    """
+    initial_world = deepcopy(world)
+    simulation = Simulate(initial_world, dims=dims)
+    # probs want to make this a while loop that stops when everything stops moving
+    for i in range(1000):
+        simulation.update(1/60.0)
+
+    final_world = []
+    for body in simulation.space._bodies:
+        final_world.append(Block(x=body.position.x, y=body.position.y))
+
+    S = not does_tower_fall(initial_world, final_world)
+    return S
+
+def infer_physics(model, conditions: dict, sites: list, num_samples: int):
+    """
+    Function to perform importance sampling on our physics model. Returns EmpiricalMarginal distribution.
+    """
+    conditioned_model = pyro.condition(model, conditions)
+    importance = Importance(conditioned_model, guide=None, num_samples=num_samples)
+    trace_posterior_conditioned = importance.run()
+    emp_marginal = EmpiricalMarginal(trace_posterior=trace_posterior_conditioned, sites=sites)
+    return emp_marginal
+
+def draw_world(world: list, dims: dict, figsize=(4,6)):
+    fig, ax = plt.subplots(1, figsize=figsize)
+    for block in world:
+        # Rectangle((bottomleftx, bottomlefty), width, height)
+        ax.add_patch(Rectangle((block.x-block.w/2, block.y-block.h/2), block.w, block.h, linewidth=1, edgecolor='k'))
+        
+    ax.set_xlim(0, dims["WORLD_WIDTH"])
+    ax.set_ylim(0, dims["WORLD_HEIGHT"])
+    ax.axhline(dims["FLOOR_HEIGHT"], color='k')
+    plt.show()
\ No newline at end of file