diff --git a/scratchpads/ak.ipynb b/scratchpads/ak.ipynb
index c70ccaff..25dbee2b 100644
--- a/scratchpads/ak.ipynb
+++ b/scratchpads/ak.ipynb
@@ -79,314 +79,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": null,
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "\n",
-       "    <div style=\"overflow:auto; background-color: white\" id=\"graph-output-3d-iH5jIY41\"></div>\n",
-       "    <script type=\"importmap\">\n",
-       "    {\"imports\": {\"three\": \"https://cdn.jsdelivr.net/npm/three@0.172.0/build/three.module.js\", \"three/addons/\": \"https://cdn.jsdelivr.net/npm/three@0.172.0/examples/jsm/\", \"d3\": \"https://cdn.jsdelivr.net/npm/d3@5.16.0/dist/d3.min.js\"}}\n",
-       "    </script>\n",
-       "    <script type=\"module\">\n",
-       "    let _settings_colors = JSON.parse('{\"edge\": \"#000000\", \"Hedge\": \"#0088ff\", \"Xedge\": \"#999999\", \"boundary\": \"#000000\", \"X\": \"#ff8888\", \"Y\": \"#aabbff\", \"Z\": \"#ccffcc\", \"H\": \"#ffff66\", \"W\": \"#000000\", \"Zalt\": \"#ccffcc\", \"Walt\": \"#000000\", \"Xdark\": \"#ff8888\", \"Ydark\": \"#aabbff\", \"Zdark\": \"#99dd99\"}');\n",
-       "    // PyZX - Python library for quantum circuit rewriting \n",
-       "//        and optimisation using the ZX-calculus\n",
-       "// Copyright (C) 2025 - Aleks Kissinger and John van de Wetering\n",
-       "\n",
-       "// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
-       "// you may not use this file except in compliance with the License.\n",
-       "// You may obtain a copy of the License at\n",
-       "\n",
-       "//    http://www.apache.org/licenses/LICENSE-2.0\n",
-       "\n",
-       "// Unless required by applicable law or agreed to in writing, software\n",
-       "// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
-       "// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
-       "// See the License for the specific language governing permissions and\n",
-       "// limitations under the License.\n",
-       "\n",
-       "import * as THREE from 'three';\n",
-       "import { Line2 } from 'three/addons/lines/Line2.js';\n",
-       "import { LineGeometry } from 'three/addons/lines/LineGeometry.js';\n",
-       "import { LineMaterial } from 'three/addons/lines/LineMaterial.js';\n",
-       "import { OrbitControls } from 'three/addons/controls/OrbitControls.js';\n",
-       "import { CSS2DRenderer, CSS2DObject } from 'three/addons/renderers/CSS2DRenderer.js';\n",
-       "\n",
-       "export function showGraph3D(tag, graph, width, height, show_labels) {\n",
-       "    const scene = new THREE.Scene();\n",
-       "    const renderer = new THREE.WebGLRenderer({ antialias: true });\n",
-       "    const labelRenderer = new CSS2DRenderer();\n",
-       "    const light = new THREE.DirectionalLight( 0xffffff, 2);\n",
-       "\n",
-       "    scene.background = new THREE.Color(0xffffff);\n",
-       "    scene.add(new THREE.AmbientLight(0xffffff, 1.5));\n",
-       "    light.position.set(1, 1, 1).normalize();\n",
-       "    scene.add(light);\n",
-       "    renderer.setSize(width, height);\n",
-       "    labelRenderer.setSize(width, height);\n",
-       "    labelRenderer.domElement.style.position = 'absolute';\n",
-       "    labelRenderer.domElement.style.top = '0px';\n",
-       "\n",
-       "    const element = document.getElementById(tag);\n",
-       "    element.appendChild(renderer.domElement);\n",
-       "    element.appendChild(labelRenderer.domElement);\n",
-       "\n",
-       "    const buttons = document.createElement('div');\n",
-       "    buttons.style.textAlign = 'center';\n",
-       "    buttons.style.fontSize = '2em';\n",
-       "    buttons.style.width = width + 'px';\n",
-       "    element.appendChild(buttons);\n",
-       "\n",
-       "    const leftButton = document.createElement('a');\n",
-       "    leftButton.href = '#';\n",
-       "    leftButton.innerHTML = '&#129092;';\n",
-       "    buttons.appendChild(leftButton);\n",
-       "\n",
-       "    const rightButton = document.createElement('a');\n",
-       "    rightButton.href = '#';\n",
-       "    rightButton.innerHTML = '&#129094;';\n",
-       "    buttons.appendChild(rightButton);\n",
-       "\n",
-       "    var ntab = {};\n",
-       "\n",
-       "    const rows = new Set();\n",
-       "    let minX = null, maxX = null, minY = null, maxY = null, minZ = null, maxZ = null;\n",
-       "\n",
-       "    graph.nodes.forEach(function(d) {\n",
-       "        ntab[d.name] = d;\n",
-       "        d.nhd = [];\n",
-       "        rows.add(d.x);\n",
-       "        minX = (minX == null) ? d.x : Math.min(d.x, minX);\n",
-       "        minY = (minY == null) ? d.y : Math.min(d.y, minY);\n",
-       "        minZ = (minZ == null) ? d.z : Math.min(d.z, minZ);\n",
-       "        maxX = (maxX == null) ? d.x : Math.max(d.x, maxX);\n",
-       "        maxY = (maxY == null) ? d.y : Math.max(d.y, maxY);\n",
-       "        maxZ = (maxZ == null) ? d.z : Math.max(d.z, maxZ);\n",
-       "\n",
-       "        let color = 0x000000, radius = 0.05;\n",
-       "        if (d.t == 1) {\n",
-       "            color = Number('0x' + '#99dd99'.substring(1));\n",
-       "            radius = 0.1;\n",
-       "        } else if (d.t == 2) {\n",
-       "            color = Number('0x' + '#ff8888'.substring(1));\n",
-       "            radius = 0.1;\n",
-       "        }\n",
-       "\n",
-       "        const geometry = new THREE.SphereGeometry(radius, 48, 24);\n",
-       "        const material = new THREE.MeshLambertMaterial({ color: color, transparent: true });\n",
-       "        d.sphere = new THREE.Mesh(geometry, material);\n",
-       "        d.sphere.name = d.name;\n",
-       "        d.sphere.position.set(d.x, d.y, d.z);\n",
-       "        d.sphere.layers.enableAll();\n",
-       "        d.sphere.renderOrder = 0.5;\n",
-       "        scene.add(d.sphere);\n",
-       "\n",
-       "        if (d.phase != '') {\n",
-       "            const phaseDiv = document.createElement('div');\n",
-       "            phaseDiv.className = 'label';\n",
-       "            phaseDiv.textContent = d.phase;\n",
-       "            phaseDiv.style.backgroundColor = 'transparent';\n",
-       "            phaseDiv.style.textAlign = 'center';\n",
-       "            phaseDiv.style.color = '#0000ff';\n",
-       "            const phaseLabel = new CSS2DObject(phaseDiv);\n",
-       "            phaseLabel.position.set(0.25, 0.5);\n",
-       "            phaseLabel.center.set(0, 0);\n",
-       "            d.sphere.add(phaseLabel);\n",
-       "            phaseLabel.layers.set(1);\n",
-       "        }\n",
-       "\n",
-       "    });\n",
-       "\n",
-       "    const rowList = [...rows].sort((a,b) => a-b);\n",
-       "    console.log(rowList);\n",
-       "\n",
-       "    graph.links.forEach(function(d) {\n",
-       "        var s = ntab[d.source];\n",
-       "        var t = ntab[d.target];\n",
-       "        d.source = s;\n",
-       "        d.target = t;\n",
-       "        s.nhd.push(t);\n",
-       "        t.nhd.push(s);\n",
-       "        let color = 0x000000;\n",
-       "        if (d.t == 2) {\n",
-       "            color = 0xffff66;\n",
-       "        }\n",
-       "\n",
-       "        const material = new LineMaterial({ color: color, linewidth: 2, transparent: true });\n",
-       "        if (s.x != t.x) { material.opacity = 0.5; }\n",
-       "        const geometry = new LineGeometry().setFromPoints([\n",
-       "            new THREE.Vector3(s.x, s.y, s.z),\n",
-       "            new THREE.Vector3(t.x, t.y, t.z)\n",
-       "        ]);\n",
-       "        d.line = new Line2(geometry, material);\n",
-       "        d.line.renderOrder = 0.6;\n",
-       "        scene.add(d.line);\n",
-       "    });\n",
-       "\n",
-       "    const highlightPlane = new THREE.Mesh(\n",
-       "        new THREE.PlaneGeometry(maxZ - minZ + 0.5, maxY - minY + 0.5),\n",
-       "        new THREE.MeshLambertMaterial({color: 0xddddff, side: THREE.DoubleSide, transparent: true}));\n",
-       "    highlightPlane.rotation.set(0,0.5*Math.PI,0);\n",
-       "    highlightPlane.position.set(0,(minY+maxY)/2, (minZ+maxZ)/2);\n",
-       "    highlightPlane.material.opacity = 0.0;\n",
-       "    highlightPlane.renderOrder = 1.0;\n",
-       "    scene.add(highlightPlane);\n",
-       "\n",
-       "    const aspect = height/width;\n",
-       "    let scale = 20;\n",
-       "    if (minX != null) {\n",
-       "        scale = Math.max((maxX - minX)/2, (maxY-minY)/(2*aspect)) + 2;\n",
-       "    }\n",
-       "    const camera = new THREE.OrthographicCamera(-scale, scale, scale*aspect, -scale*aspect);\n",
-       "    camera.layers.enableAll();\n",
-       "    camera.position.z = 5;\n",
-       "    if (minX != null) {\n",
-       "        camera.position.z = 2*Math.max(maxX, maxY, maxZ);\n",
-       "    }\n",
-       "\n",
-       "    const controls = new OrbitControls(camera, labelRenderer.domElement);\n",
-       "    const raycaster = new THREE.Raycaster();\n",
-       "    const mouse = new THREE.Vector2();\n",
-       "    let highlightRow = -1;\n",
-       "    controls.minDistance = 1;\n",
-       "    controls.maxDistance = 100;\n",
-       "\n",
-       "\n",
-       "\n",
-       "    function checkIntersection() {\n",
-       "        raycaster.setFromCamera(mouse, camera);\n",
-       "        const intersects = raycaster.intersectObject(scene, true);\n",
-       "        highlightRow = -1;\n",
-       "        for (let obj of intersects) {\n",
-       "            const selectedObject = obj.object;\n",
-       "            if (Object.hasOwn(selectedObject, 'name') && selectedObject.name != '') {\n",
-       "                const d = ntab[selectedObject.name];\n",
-       "                highlightRow = rowList.indexOf(d.x);\n",
-       "                break;\n",
-       "            }\n",
-       "        }\n",
-       "        update();\n",
-       "    }\n",
-       "\n",
-       "\n",
-       "    function update() {\n",
-       "        if (highlightRow == -1) {\n",
-       "            highlightPlane.material.opacity = 0.0;\n",
-       "        } else {\n",
-       "            highlightPlane.position.setComponent(0, rowList[highlightRow]);\n",
-       "            highlightPlane.material.opacity = 0.5;\n",
-       "        }\n",
-       "\n",
-       "        graph.nodes.forEach(function (d) {\n",
-       "            if (highlightRow == -1 || rowList[highlightRow] == d.x) {\n",
-       "                d.sphere.material.opacity = 1.0;\n",
-       "                d.sphere.renderOrder = 0.5;\n",
-       "            } else {\n",
-       "                d.sphere.material.opacity = 0.4;\n",
-       "                d.sphere.renderOrder = 0.7;\n",
-       "            }\n",
-       "        });\n",
-       "\n",
-       "        graph.links.forEach(function (d) {\n",
-       "            if (highlightRow == -1 || (rowList[highlightRow] == d.target.x && rowList[highlightRow] == d.source.x)) {\n",
-       "                if (d.source.x != d.target.x) {\n",
-       "                    d.line.material.opacity = 0.5;\n",
-       "                } else {\n",
-       "                    d.line.material.opacity = 1.0;\n",
-       "                }\n",
-       "                d.line.renderOrder = 0.6;\n",
-       "            } else {\n",
-       "                d.line.material.opacity = 0.25;\n",
-       "                d.line.renderOrder = 0.8;\n",
-       "            }\n",
-       "        });\n",
-       "    }\n",
-       "\n",
-       "    let mouseX = 0;\n",
-       "    let mouseY = 0;\n",
-       "\n",
-       "    function onMouseDown(event) {\n",
-       "        mouseX = event.clientX;\n",
-       "        mouseY = event.clientY;\n",
-       "    }\n",
-       "    \n",
-       "    function onMouseUp(event) {\n",
-       "        if (event.isPrimary === false) return;\n",
-       "        const dx = event.clientX - mouseX;\n",
-       "        const dy = event.clientY - mouseY;\n",
-       "\n",
-       "        if (dx == 0 && dy == 0) {\n",
-       "            const rect = element.getBoundingClientRect();\n",
-       "            const x = event.clientX - rect.left;\n",
-       "            const y = event.clientY - rect.top;\n",
-       "\n",
-       "            mouse.x = ((x / width) * 2 - 1);\n",
-       "            mouse.y = (-(y / height) * 2 + 1);\n",
-       "            checkIntersection();\n",
-       "        }\n",
-       "    }\n",
-       "\n",
-       "    function goLeft() {\n",
-       "        if (rowList.length > 0) {\n",
-       "            if (highlightRow == -1) {\n",
-       "                highlightRow = rowList.length - 1;\n",
-       "            } else {\n",
-       "                if (highlightRow == 0) {\n",
-       "                    highlightRow = rowList.length - 1;\n",
-       "                } else {\n",
-       "                    highlightRow = highlightRow - 1;\n",
-       "                }\n",
-       "            }\n",
-       "        }\n",
-       "        update();\n",
-       "    }\n",
-       "\n",
-       "    function goRight() {\n",
-       "        if (rowList.length > 0) {\n",
-       "            if (highlightRow == -1) {\n",
-       "                highlightRow = 0;\n",
-       "            } else {\n",
-       "                highlightRow = (highlightRow + 1) % rowList.length;\n",
-       "            }\n",
-       "        }\n",
-       "        update();\n",
-       "    }\n",
-       "\n",
-       "    labelRenderer.domElement.addEventListener('mousedown', onMouseDown);\n",
-       "    labelRenderer.domElement.addEventListener('mouseup', onMouseUp);\n",
-       "    leftButton.addEventListener('click', goLeft);\n",
-       "    rightButton.addEventListener('click', goRight);\n",
-       "    labelRenderer.tabIndex = 0;\n",
-       "\n",
-       "    function animate() {\n",
-       "        renderer.render(scene, camera);\n",
-       "        labelRenderer.render(scene, camera);\n",
-       "    }\n",
-       "    renderer.setAnimationLoop(animate);\n",
-       "}\n",
-       "\n",
-       "    showGraph3D('graph-output-3d-iH5jIY41', JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": -5.5, \"y\": -1.0, \"z\": -1.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": -5.5, \"y\": 0.0, \"z\": -1.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": -5.5, \"y\": 1.0, \"z\": -1.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": -5.5, \"y\": -1.0, \"z\": 0.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": -5.5, \"y\": 0.0, \"z\": 0.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": -5.5, \"y\": 1.0, \"z\": 0.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": -5.5, \"y\": -1.0, \"z\": 1.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": -5.5, \"y\": 0.0, \"z\": 1.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": -5.5, \"y\": 1.0, \"z\": 1.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": -4.5, \"y\": 1.0, \"z\": 0.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": -4.5, \"y\": 1.0, \"z\": 1.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": -3.5, \"y\": 0.0, \"z\": 1.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": -3.5, \"y\": 1.0, \"z\": 1.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": -4.5, \"y\": 0.0, \"z\": -1.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": -4.5, \"y\": 0.0, \"z\": 0.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": -3.5, \"y\": 1.0, \"z\": 0.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": -3.5, \"y\": 0.0, \"z\": 0.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": -2.5, \"y\": 0.0, \"z\": 0.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": -2.5, \"y\": 1.0, \"z\": 0.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": -2.5, \"y\": 1.0, \"z\": 1.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": -2.5, \"y\": 0.0, \"z\": 1.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": -4.5, \"y\": -1.0, \"z\": 0.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": -4.5, \"y\": -1.0, \"z\": 1.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": -1.5, \"y\": 0.0, \"z\": -1.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": -1.5, \"y\": 0.0, \"z\": 0.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": -1.5, \"y\": 1.0, \"z\": 0.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": -1.5, \"y\": 1.0, \"z\": -1.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": -0.5, \"y\": 1.0, \"z\": 0.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": -0.5, \"y\": 1.0, \"z\": -1.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": -3.5, \"y\": -1.0, \"z\": 0.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": -3.5, \"y\": -1.0, \"z\": -1.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": 0.5, \"y\": 1.0, \"z\": 0.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": 0.5, \"y\": 1.0, \"z\": 1.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": 1.5, \"y\": 0.0, \"z\": 0.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": 1.5, \"y\": 1.0, \"z\": 0.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": 0.5, \"y\": 0.0, \"z\": -1.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": 0.5, \"y\": 1.0, \"z\": -1.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": -2.5, \"y\": -1.0, \"z\": 1.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": -2.5, \"y\": -1.0, \"z\": 0.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": 1.5, \"y\": 0.0, \"z\": -1.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": 1.5, \"y\": 1.0, \"z\": -1.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": 2.5, \"y\": 0.0, \"z\": -1.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": 2.5, \"y\": 1.0, \"z\": -1.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": 2.5, \"y\": 0.0, \"z\": 0.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": 2.5, \"y\": -1.0, \"z\": 0.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"45\", \"x\": 3.5, \"y\": 0.0, \"z\": 0.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"46\", \"x\": 3.5, \"y\": 0.0, \"z\": 1.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"47\", \"x\": 4.5, \"y\": 0.0, \"z\": 0.0, \"t\": 2, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"48\", \"x\": 4.5, \"y\": 0.0, \"z\": -1.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"49\", \"x\": 5.5, \"y\": -1.0, \"z\": -1.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"50\", \"x\": 5.5, \"y\": 0.0, \"z\": -1.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"51\", \"x\": 5.5, \"y\": 1.0, \"z\": -1.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"52\", \"x\": 5.5, \"y\": -1.0, \"z\": 0.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"53\", \"x\": 5.5, \"y\": 0.0, \"z\": 0.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"54\", \"x\": 5.5, \"y\": 1.0, \"z\": 0.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"55\", \"x\": 5.5, \"y\": -1.0, \"z\": 1.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"56\", \"x\": 5.5, \"y\": 0.0, \"z\": 1.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"57\", \"x\": 5.5, \"y\": 1.0, \"z\": 1.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}], \"links\": [{\"source\": \"0\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"1\", \"target\": \"13\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"2\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"3\", \"target\": \"21\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"5\", \"target\": \"9\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"6\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"7\", \"target\": \"11\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"8\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"10\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"9\", \"target\": \"15\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"10\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"12\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"11\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"12\", \"target\": \"19\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"14\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"13\", \"target\": \"23\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"14\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"16\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"15\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"16\", \"target\": \"17\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"18\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"17\", \"target\": \"24\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"18\", \"target\": \"25\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"20\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"19\", \"target\": \"32\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"20\", \"target\": \"46\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"21\", \"target\": \"22\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"21\", \"target\": \"29\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"22\", \"target\": \"37\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"23\", \"target\": \"24\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"23\", \"target\": \"35\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"24\", \"target\": \"33\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"26\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"25\", \"target\": \"27\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"26\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"28\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"27\", \"target\": \"31\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"28\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"30\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"29\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"30\", \"target\": \"49\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"32\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"31\", \"target\": \"34\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"32\", \"target\": \"57\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"33\", \"target\": \"34\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"33\", \"target\": \"43\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"34\", \"target\": \"54\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"35\", \"target\": \"36\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"35\", \"target\": \"39\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"36\", \"target\": \"40\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"37\", \"target\": \"38\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"37\", \"target\": \"55\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"38\", \"target\": \"44\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"40\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"39\", \"target\": \"41\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"40\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"42\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"41\", \"target\": \"48\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"42\", \"target\": \"51\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"44\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"43\", \"target\": \"45\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"44\", \"target\": \"52\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"46\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"45\", \"target\": \"47\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"46\", \"target\": \"56\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"47\", \"target\": \"48\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"47\", \"target\": \"53\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"48\", \"target\": \"50\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 1000, 500, false);\n",
-       "    </script>\n",
-       "    "
-      ],
-      "text/plain": [
-       "<IPython.core.display.HTML object>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "outputs": [],
    "source": [
     "zx.draw_3d(g)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -400,7 +102,7 @@
     "    vs = [[g.add_vertex(B, row=x, qubit=y) for _ in zrange] for y in yrange]\n",
     "    for y in yrange:\n",
     "        for z in zrange:\n",
-    "            g.set_vdata(vs[y][z], 'z', z)\n",
+    "            g.set_vdata(vs[y-yrange.start][z-zrange.start], 'z', z)\n",
     "    return vs\n",
     "\n",
     "def add_patch(g, ty, x, yrange, zrange, orientation='H'):\n",
@@ -409,28 +111,59 @@
     "    parity = 0 if ty == Z else 1\n",
     "    for y in range(yrange.start, yrange.stop+1):\n",
     "        for z in range(zrange.start, zrange.stop+1):\n",
-    "            if y in yrange and z in zrange: g.set_vdata(vs[y][z], 'z', z)\n",
-    "            if orientation == 'H' and (y == yrange.start or y == yrange.stop): continue\n",
-    "            if orientation == 'V' and (z == zrange.start or z == zrange.stop): continue\n",
+    "            if y in yrange and z in zrange: g.set_vdata(vs[y-yrange.start][z-zrange.start], 'z', z)\n",
+    "    \n",
+    "            if y == yrange.start: yshift = -0.3\n",
+    "            elif y == yrange.stop: yshift = -0.7\n",
+    "            else: yshift = -0.5\n",
+    "\n",
+    "            if z == zrange.start: zshift = -0.3\n",
+    "            elif z == zrange.stop: zshift = -0.7\n",
+    "            else: zshift = -0.5\n",
+    "                \n",
+    "            if (orientation == 'H' and yshift != -0.5) or (orientation == 'V' and zshift != -0.5):\n",
+    "                continue\n",
+    "            \n",
     "            if (y+z) % 2 == parity:\n",
-    "                w = g.add_vertex(ty_op, row=x, qubit=y-0.5)\n",
-    "                g.set_vdata(w, 'z', z-0.5)\n",
+    "                w = g.add_vertex(ty_op, row=x, qubit=y+yshift)\n",
+    "                g.set_vdata(w, 'z', z+zshift)\n",
     "                for (i,j) in ((y-1, z-1), (y, z-1), (y-1, z), (y, z)):\n",
     "                    if i in yrange and j in zrange:\n",
-    "                        g.add_edge((w, vs[i][j]))\n",
+    "                        g.add_edge((w, vs[i-yrange.start][j-zrange.start]))\n",
     "    return vs"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "g = zx.Graph()\n",
+    "sz = range(0,3)\n",
+    "x = 0\n",
+    "p1 = add_boundary(g, x, sz, sz); x += 2\n",
+    "for _ in range(3):\n",
+    "    p = add_patch(g, Z, x, sz, sz, 'H'); x += 1\n",
+    "    connect(g, p1, p)\n",
+    "    p1 = add_patch(g, X, x, sz, sz, 'V'); x += 2\n",
+    "    connect(g, p, p1)\n",
+    "p = add_boundary(g, x, sz, sz)\n",
+    "connect(g, p1, p)\n",
+    "\n",
+    "zx.draw_3d(g)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/html": [
        "\n",
-       "    <div style=\"overflow:auto; background-color: white\" id=\"graph-output-3d-xQtZJvw3\"></div>\n",
+       "    <div style=\"overflow:auto; background-color: white\" id=\"graph-output-3d-IVcQEq72\"></div>\n",
        "    <script type=\"importmap\">\n",
        "    {\"imports\": {\"three\": \"https://cdn.jsdelivr.net/npm/three@0.172.0/build/three.module.js\", \"three/addons/\": \"https://cdn.jsdelivr.net/npm/three@0.172.0/examples/jsm/\", \"d3\": \"https://cdn.jsdelivr.net/npm/d3@5.16.0/dist/d3.min.js\"}}\n",
        "    </script>\n",
@@ -712,7 +445,7 @@
        "    renderer.setAnimationLoop(animate);\n",
        "}\n",
        "\n",
-       "    showGraph3D('graph-output-3d-xQtZJvw3', JSON.parse('{\"nodes\": [{\"name\": \"0\", \"x\": -4.0, \"y\": -2.0, \"z\": -2.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"1\", \"x\": -4.0, \"y\": -2.0, \"z\": -1.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"2\", \"x\": -4.0, \"y\": -2.0, \"z\": 0.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"3\", \"x\": -4.0, \"y\": -2.0, \"z\": 1.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"4\", \"x\": -4.0, \"y\": -2.0, \"z\": 2.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"5\", \"x\": -4.0, \"y\": -1.0, \"z\": -2.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"6\", \"x\": -4.0, \"y\": -1.0, \"z\": -1.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"7\", \"x\": -4.0, \"y\": -1.0, \"z\": 0.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"8\", \"x\": -4.0, \"y\": -1.0, \"z\": 1.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"9\", \"x\": -4.0, \"y\": -1.0, \"z\": 2.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"10\", \"x\": -4.0, \"y\": 0.0, \"z\": -2.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"11\", \"x\": -4.0, \"y\": 0.0, \"z\": -1.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"12\", \"x\": -4.0, \"y\": 0.0, \"z\": 0.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"13\", \"x\": -4.0, \"y\": 0.0, \"z\": 1.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"14\", \"x\": -4.0, \"y\": 0.0, \"z\": 2.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"15\", \"x\": -4.0, \"y\": 1.0, \"z\": -2.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"16\", \"x\": -4.0, \"y\": 1.0, \"z\": -1.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"17\", \"x\": -4.0, \"y\": 1.0, \"z\": 0.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"18\", \"x\": -4.0, \"y\": 1.0, \"z\": 1.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"19\", \"x\": -4.0, \"y\": 1.0, \"z\": 2.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"20\", \"x\": -4.0, \"y\": 2.0, \"z\": -2.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"21\", \"x\": -4.0, \"y\": 2.0, \"z\": -1.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"22\", \"x\": -4.0, \"y\": 2.0, \"z\": 0.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"23\", \"x\": -4.0, \"y\": 2.0, \"z\": 1.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"24\", \"x\": -4.0, \"y\": 2.0, \"z\": 2.0, \"t\": 0, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"25\", \"x\": -2.0, \"y\": -2.0, \"z\": -2.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"26\", \"x\": -2.0, \"y\": -2.0, \"z\": -1.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"27\", \"x\": -2.0, \"y\": -2.0, \"z\": 0.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"28\", \"x\": -2.0, \"y\": -2.0, \"z\": 1.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"29\", \"x\": -2.0, \"y\": -2.0, \"z\": 2.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"30\", \"x\": -2.0, \"y\": -1.0, \"z\": -2.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"31\", \"x\": -2.0, \"y\": -1.0, \"z\": -1.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"32\", \"x\": -2.0, \"y\": -1.0, \"z\": 0.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"33\", \"x\": -2.0, \"y\": -1.0, \"z\": 1.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"34\", \"x\": -2.0, \"y\": -1.0, \"z\": 2.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"35\", \"x\": -2.0, \"y\": 0.0, \"z\": -2.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"36\", \"x\": -2.0, \"y\": 0.0, \"z\": -1.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"37\", \"x\": -2.0, \"y\": 0.0, \"z\": 0.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"38\", \"x\": -2.0, \"y\": 0.0, \"z\": 1.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"39\", \"x\": -2.0, \"y\": 0.0, \"z\": 2.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"40\", \"x\": -2.0, \"y\": 1.0, \"z\": -2.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"41\", \"x\": -2.0, \"y\": 1.0, \"z\": -1.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"42\", \"x\": -2.0, \"y\": 1.0, \"z\": 0.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"43\", \"x\": -2.0, \"y\": 1.0, \"z\": 1.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"44\", \"x\": -2.0, \"y\": 1.0, \"z\": 2.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"45\", \"x\": -2.0, \"y\": 2.0, \"z\": -2.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"46\", \"x\": -2.0, \"y\": 2.0, \"z\": -1.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"47\", \"x\": -2.0, \"y\": 2.0, \"z\": 0.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"48\", \"x\": -2.0, \"y\": 2.0, \"z\": 1.0, \"t\": 1, \"phase\": \"\", \"ground\": false, \"vdata\": []}, {\"name\": \"49\", \"x\": -2.0, \"y\": 2.0, \"z\": 2.0, \"t\": 1, \"phase\": \"\", 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\"num_parallel\": 1}, {\"source\": \"4100\", \"target\": \"4250\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4101\", \"target\": \"4168\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4101\", \"target\": \"4174\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4101\", \"target\": \"4251\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4102\", \"target\": \"4168\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4102\", \"target\": \"4175\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4102\", \"target\": \"4252\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4103\", \"target\": \"4169\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4103\", \"target\": \"4175\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4103\", \"target\": \"4253\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4104\", \"target\": \"4169\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4104\", \"target\": \"4176\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4104\", \"target\": \"4254\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4105\", \"target\": \"4170\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4105\", \"target\": \"4176\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4105\", \"target\": \"4255\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4106\", \"target\": \"4170\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4106\", \"target\": \"4177\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4106\", \"target\": \"4256\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4107\", \"target\": \"4171\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4107\", \"target\": \"4177\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4107\", \"target\": \"4257\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4108\", \"target\": \"4171\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4108\", \"target\": \"4178\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4108\", \"target\": \"4258\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4109\", \"target\": \"4172\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4109\", \"target\": \"4178\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4109\", \"target\": \"4259\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4110\", \"target\": \"4172\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4110\", \"target\": \"4179\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4110\", \"target\": \"4260\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4111\", \"target\": \"4173\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4111\", \"target\": \"4179\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4111\", \"target\": \"4261\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4112\", \"target\": \"4173\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4112\", \"target\": \"4262\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4113\", \"target\": \"4180\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4113\", \"target\": \"4263\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4114\", \"target\": \"4174\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4114\", \"target\": \"4180\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4114\", \"target\": \"4264\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4115\", \"target\": \"4174\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4115\", \"target\": \"4181\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4115\", \"target\": \"4265\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4116\", \"target\": \"4175\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4116\", \"target\": \"4181\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4116\", \"target\": \"4266\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4117\", \"target\": \"4175\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4117\", \"target\": \"4182\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4117\", \"target\": \"4267\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4118\", \"target\": \"4176\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4118\", \"target\": \"4182\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4118\", \"target\": \"4268\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4119\", \"target\": \"4176\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4119\", \"target\": \"4183\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4119\", \"target\": \"4269\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4120\", \"target\": \"4177\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4120\", \"target\": \"4183\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4120\", \"target\": \"4270\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4121\", \"target\": \"4177\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4121\", \"target\": \"4184\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4121\", \"target\": \"4271\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4122\", \"target\": \"4178\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4122\", \"target\": \"4184\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4122\", \"target\": \"4272\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4123\", \"target\": \"4178\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4123\", \"target\": \"4185\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4123\", \"target\": \"4273\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4124\", \"target\": \"4179\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4124\", \"target\": \"4185\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4124\", \"target\": \"4274\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4125\", \"target\": \"4179\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4125\", \"target\": \"4186\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4125\", \"target\": \"4275\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4126\", \"target\": \"4186\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4126\", \"target\": \"4276\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4127\", \"target\": \"4180\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4127\", \"target\": \"4277\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4128\", \"target\": \"4180\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4128\", \"target\": \"4187\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4128\", \"target\": \"4278\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4129\", \"target\": \"4181\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4129\", \"target\": \"4187\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4129\", \"target\": \"4279\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4130\", \"target\": \"4181\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4130\", \"target\": \"4188\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4130\", \"target\": \"4280\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4131\", \"target\": \"4182\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4131\", \"target\": \"4188\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4131\", \"target\": \"4281\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4132\", \"target\": \"4182\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4132\", \"target\": \"4189\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4132\", \"target\": \"4282\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4133\", \"target\": \"4183\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4133\", \"target\": \"4189\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4133\", \"target\": \"4283\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4134\", \"target\": \"4183\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4134\", \"target\": \"4190\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4134\", \"target\": \"4284\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4135\", \"target\": \"4184\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4135\", \"target\": \"4190\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4135\", \"target\": \"4285\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4136\", \"target\": \"4184\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4136\", \"target\": \"4191\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4136\", \"target\": \"4286\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4137\", \"target\": \"4185\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4137\", \"target\": \"4191\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4137\", \"target\": \"4287\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4138\", \"target\": \"4185\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4138\", \"target\": \"4192\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4138\", \"target\": \"4288\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4139\", \"target\": \"4186\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4139\", \"target\": \"4192\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4139\", \"target\": \"4289\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4140\", \"target\": \"4186\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}, {\"source\": \"4140\", \"target\": \"4290\", \"t\": 1, \"index\": 0, \"num_parallel\": 1}], \"pauli_web\": []}'), 1000, 500, false);\n",
        "    </script>\n",
        "    "
       ],
@@ -726,27 +459,57 @@
    ],
    "source": [
     "g = zx.Graph()\n",
-    "sz = range(0,5)\n",
+    "d = 7\n",
     "x = 0\n",
-    "p1 = add_boundary(g, x, sz, sz); x += 2\n",
-    "for _ in range(2):\n",
-    "    p = add_patch(g, Z, x, sz, sz, 'H'); x += 1\n",
-    "    connect(g, p1, p)\n",
-    "    p1 = add_patch(g, X, x, sz, sz, 'V'); x += 2\n",
+    "\n",
+    "p = add_boundary(g, x, range(0,d), range(0,2*d))\n",
+    "\n",
+    "x += d\n",
+    "\n",
+    "for _ in range(d):\n",
+    "    x += 0.7 * (d/(d+1))\n",
+    "    p1a = add_patch(g, Z, x, range(0,d), range(0,d), 'H')\n",
+    "    p1b = add_patch(g, Z, x, range(0,d), range(d,2*d), 'H')\n",
+    "    p1 = [q+r for q,r in zip(p1a,p1b)]\n",
     "    connect(g, p, p1)\n",
-    "p = add_boundary(g, x, sz, sz)\n",
-    "connect(g, p1, p)\n",
+    "    p = p1\n",
+    "    \n",
+    "    x += 0.3 * (d/(d+1))\n",
+    "    p1a = add_patch(g, X, x, range(0,d), range(0,d), 'V')\n",
+    "    p1b = add_patch(g, X, x, range(0,d), range(d,2*d), 'V')\n",
+    "    p1 = [q+r for q,r in zip(p1a,p1b)]\n",
+    "    connect(g, p, p1)\n",
+    "    p = p1\n",
+    "\n",
+    "x += d\n",
+    "\n",
+    "for _ in range(d):\n",
+    "    x += 0.7 * (d/(d+1))\n",
+    "    p1 = add_patch(g, Z, x, range(0,d), range(0,2*d), 'H')\n",
+    "    connect(g, p, p1)\n",
+    "    p = p1\n",
+    "    \n",
+    "    x += 0.3 * (d/(d+1))\n",
+    "    p1 = add_patch(g, X, x, range(0,d), range(0,2*d), 'V')\n",
+    "    connect(g, p, p1)\n",
+    "    p = p1\n",
+    "\n",
+    "x += d\n",
+    "\n",
+    "p1 = add_boundary(g, x, range(0,d), range(0,2*d))\n",
+    "connect(g, p, p1)\n",
+    "p = p1\n",
+    "\n",
+    "for v in g.vertices():\n",
+    "    z = g.vdata(v, 'z')\n",
+    "    if z == d-0.5:\n",
+    "        g.set_vdata(v, 'z', z+(d/2))\n",
+    "    elif z > d-0.5:\n",
+    "        g.set_vdata(v, 'z', z+d)\n",
     "\n",
     "zx.draw_3d(g)"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  },
   {
    "cell_type": "code",
    "execution_count": null,