MCMC_dynamics.ipynb

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  {
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   "source": [
    "# Sphere Packing"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ca5e7e1",
   "metadata": {},
   "source": [
    "### Carpa de Melquíades, oct 2022\n",
    "#### Krystifer Campos - Universidad del Valle"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "10a4ec6c",
   "metadata": {},
   "source": [
    "----------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2be28f50",
   "metadata": {},
   "source": [
    "Ideal gases, or the atomic structure of condensed matter, can be modeled to a first approximation from a classical point of view. Consider finite solid spheres inside a cube, like billiard balls (usually called discs if they are in two dimensions). We can model the dynamics of the system using the equations of kinematics and conservation of linear momentum, but we can also approximate from statistics. In this code, the MCMC (Markov Chain Monte Carlo) algorithm is performed to show the characteristic of the packing of spheres. The base of this code is the book : Algorithms and Computations by Werner Krauth, and the Coursera Course [Statistical Mechanics: Algorithms and Computations](https://www.coursera.org/?skipBrowseRedirect=true)."
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   "cell_type": "markdown",
   "id": "4b44bdef",
   "metadata": {},
   "source": [
    "-----------------------------------------------------------------------------------------------------------------"
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  {
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   "execution_count": 1,
   "id": "e950d7df",
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib\n",
    "from matplotlib import animation\n",
    "from matplotlib.animation import PillowWriter\n",
    "import random, math\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "%matplotlib notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d402b9c",
   "metadata": {},
   "source": [
    "### Initial conditions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2565d967",
   "metadata": {},
   "source": [
    "To generate the initial configuration, we randomly assign (with uniform probability) the position of N particles on a three and two-dimensional grid. Each particle has a radius \"sigma\", whenever the distance between centres is less than twice the radius, there is an overlap. Overlaps are not allowed, so we apply the \"Tabula rasa\" rule, this is, to clear up the entire configuration and start from scratch. This procedure, though slow is consistent with the principle of having an equal probability for each possible configuration as an initial condition."
   ]
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   "cell_type": "code",
   "execution_count": 2,
   "id": "9b4e6e46",
   "metadata": {},
   "outputs": [],
   "source": [
    "def direct_disks_box2D(N, sigma):               #Generate initial condition with equal probability in 2D\n",
    "    condition = False\n",
    "    while condition == False:\n",
    "        L = [(random.uniform(sigma, 1.0 - sigma), random.uniform(sigma, 1.0 - sigma))]\n",
    "        for k in range(1, N):\n",
    "            a = (random.uniform(sigma, 1.0 - sigma), random.uniform(sigma, 1.0 - sigma))\n",
    "            min_dist = min(math.sqrt((a[0] - b[0]) ** 2 + (a[1] - b[1]) ** 2) for b in L) \n",
    "            if min_dist < 2.0 * sigma: \n",
    "                condition = False\n",
    "                break\n",
    "            else:\n",
    "                L.append(a)\n",
    "                condition = True\n",
    "    return L"
   ]
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  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "22177e69",
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   "source": [
    "def direct_disks_box3D(N, sigma):               #Generate initial condition with equal probability in 3D\n",
    "    condition = False\n",
    "    while condition == False:\n",
    "        L = [(random.uniform(sigma, 1.0 - sigma), random.uniform(sigma, 1.0 - sigma), random.uniform(sigma, 1.0 - sigma))]\n",
    "        for k in range(1, N):\n",
    "            a = (random.uniform(sigma, 1.0 - sigma), random.uniform(sigma, 1.0 - sigma),  random.uniform(sigma, 1.0 - sigma))\n",
    "            min_dist = min(math.sqrt((a[0] - b[0]) ** 2 + (a[1] - b[1]) ** 2 + (a[2] - b[2]) ** 2) for b in L) \n",
    "            if min_dist < 2.0 * sigma: \n",
    "                condition = False\n",
    "                break\n",
    "            else:\n",
    "                L.append(a)\n",
    "                condition = True\n",
    "    return L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b775b664",
   "metadata": {},
   "outputs": [],
   "source": [
    "def drawSphere(xCenter, yCenter, zCenter, r):          # Function to draw spheres\n",
    "    #draw sphere\n",
    "    u, v = np.mgrid[0:2*np.pi:100j, 0:np.pi:50j]\n",
    "    x=np.cos(u)*np.sin(v)\n",
    "    y=np.sin(u)*np.sin(v)\n",
    "    z=np.cos(v)\n",
    "    # shift and scale sphere\n",
    "    x = r*x + xCenter\n",
    "    y = r*y + yCenter\n",
    "    z = r*z + zCenter\n",
    "    return (x,y,z)"
   ]
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   "source": [
    "-------------------------------------------------------------------------------------"
   ]
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  {
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   "source": [
    "### Animation and method"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42601995",
   "metadata": {},
   "source": [
    "Once the initial configuration is set, we create Markov Chains by changing the position of a random sphere by a random number in each coordinate, being this number in a finite interval (-delta, delta).  In each event, we check for overlaps, if overlap occurs we let the configuration equal and repeat the random process. We also check each particle inside the box, for example, in the two-dimensional case, the x and y components must be within the range (sigma, 1-sigma). The animation is done by merging successive snapshots of the system in gif format."
   ]
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  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "d537a320",
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   "source": [
    "def animate(i):\n",
    "    ax.set_xlim(0,1)\n",
    "    ax.set_ylim(0,1)\n",
    "    a = random.choice(L)\n",
    "    b = np.asarray([a[0] + random.uniform(-delta, delta), a[1] + random.uniform(-delta, delta)])\n",
    "    min_dist = min((b[0] - c[0]) ** 2 + (b[1] - c[1]) ** 2 for c in L if c[0] != a[0] and c[1] !=a[1]) \n",
    "    box_cond = min(b[0], b[1]) < sigma or max(b[0], b[1]) > 1.0 - sigma\n",
    "    if not (box_cond or min_dist < 4.0 * sigma ** 2):\n",
    "        a[:] = b\n",
    "        L[L==a]=b\n",
    "        ax.clear()\n",
    "        circles = [plt.Circle((xi,yi), radius = sigma, linewidth = 0.1) for xi,yi in zip(L[:,0],L[:,1])]\n",
    "        circlesCollect = matplotlib.collections.PatchCollection(circles, facecolors = colors)\n",
    "        ax.add_collection(circlesCollect)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0bc4daae",
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    "scrolled": true
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       "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', { width: x_pixels, height: y_pixels });\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_message = function (type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function () {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function (fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n",
       "    fig.rubberband_canvas.style.cursor = msg['cursor'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_message = function (fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message('ack', {});\n",
       "};\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function (fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            var img = evt.data;\n",
       "            if (img.type !== 'image/png') {\n",
       "                /* FIXME: We get \"Resource interpreted as Image but\n",
       "                 * transferred with MIME type text/plain:\" errors on\n",
       "                 * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "                 * to be part of the websocket stream */\n",
       "                img.type = 'image/png';\n",
       "            }\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src\n",
       "                );\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                img\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig['handle_' + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "};\n",
       "\n",
       "// from https://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function (e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e) {\n",
       "        e = window.event;\n",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n",
       "\n",
       "    return { x: x, y: y };\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * https://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys(original) {\n",
       "    return Object.keys(original).reduce(function (obj, key) {\n",
       "        if (typeof original[key] !== 'object') {\n",
       "            obj[key] = original[key];\n",
       "        }\n",
       "        return obj;\n",
       "    }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function (event, name) {\n",
       "    var canvas_pos = mpl.findpos(event);\n",
       "\n",
       "    if (name === 'button_press') {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.key_event = function (event, name) {\n",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.key === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.key;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.key !== 'Control') {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    else if (event.altKey && event.key !== 'Alt') {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    else if (event.shiftKey && event.key !== 'Shift') {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k' + event.key;\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n",
       "    if (name === 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message('toolbar_button', { name: name });\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "\n",
       "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
       "// prettier-ignore\n",
       "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "var comm_websocket_adapter = function (comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.binaryType = comm.kernel.ws.binaryType;\n",
       "    ws.readyState = comm.kernel.ws.readyState;\n",
       "    function updateReadyState(_event) {\n",
       "        if (comm.kernel.ws) {\n",
       "            ws.readyState = comm.kernel.ws.readyState;\n",
       "        } else {\n",
       "            ws.readyState = 3; // Closed state.\n",
       "        }\n",
       "    }\n",
       "    comm.kernel.ws.addEventListener('open', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('close', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('error', updateReadyState);\n",
       "\n",
       "    ws.close = function () {\n",
       "        comm.close();\n",
       "    };\n",
       "    ws.send = function (m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function (msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        var data = msg['content']['data'];\n",
       "        if (data['blob'] !== undefined) {\n",
       "            data = {\n",
       "                data: new Blob(msg['buffers'], { type: data['blob'] }),\n",
       "            };\n",
       "        }\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(data);\n",
       "    });\n",
       "    return ws;\n",
       "};\n",
       "\n",
       "mpl.mpl_figure_comm = function (comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element;\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error('Failed to find cell for figure', id, fig);\n",
       "        return;\n",
       "    }\n",
       "    fig.cell_info[0].output_area.element.on(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "    fig.resizeObserverInstance.unobserve(fig.canvas_div);\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable();\n",
       "    fig.parent_element.innerHTML =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "    fig.close_ws(fig, msg);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.close_ws = function (fig, msg) {\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message('ack', {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    if (event.target !== this) {\n",
       "        // Ignore bubbled events from children.\n",
       "        return;\n",
       "    }\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('tabindex', 0);\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "mpl.find_output_cell = function (html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i = 0; i < ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code') {\n",
       "            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] === html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "};\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel !== null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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\" width=\"500\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig2d, ax = plt.subplots(1,1, figsize=(5,5))                #Animation for 2D hard disks\n",
    "N=5\n",
    "sigma = 0.05\n",
    "delta = 0.2\n",
    "colors = ['r', 'b', 'g', 'orange', 'gray', 'olive', 'gold', 'teal', 'chocolate', 'crimson', 'purple', 'lime']\n",
    "L = np.asarray(direct_disks_box2D(N, sigma))\n",
    "ani = animation.FuncAnimation(fig2d, animate, frames=800, interval = 0.1)\n",
    "#ani.save('yourpath/mcmc2D.gif', writer = 'pillow', dpi = 100) "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cec46ed3",
   "metadata": {},
   "source": [
    "The animation for 3-dimensional disks is the same, just adding an extra coordinate and drawing the points as spheres."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "edd824fe",
   "metadata": {},
   "outputs": [],
   "source": [
    "def animate(i):\n",
    "    a = random.choice(L)\n",
    "    b = np.asarray([a[0] + random.uniform(-delta, delta), a[1] + random.uniform(-delta, delta),  a[2] + random.uniform(-delta, delta)])\n",
    "    min_dist = min((b[0] - c[0]) ** 2 + (b[1] - c[1]) ** 2 + (b[2] - c[2]) ** 2 for c in L if (c[0] != a[0] and c[1] !=a[1] and c[2] !=a[2])) \n",
    "    box_cond = (b[0]<sigma or b[1]<sigma or b[2]<sigma) or (b[0]>1.0-sigma or b[1]>1.0-sigma or b[2]>1.0-sigma)\n",
    "    ax.view_init(elev=10., azim=i)\n",
    "    if not (box_cond or min_dist < 2* sigma):\n",
    "        a[:] = b\n",
    "        L[L==a]=b\n",
    "        ax.clear()\n",
    "        for k in range(N):\n",
    "            ax.set_xlim(0,1)\n",
    "            ax.set_ylim(0,1)\n",
    "            ax.set_zlim(0,1)\n",
    "            (x,y,z) = drawSphere(L[:,0][k],L[:,1][k],L[:,2][k],sigma)\n",
    "            ax.plot_surface(x, y, z, cmap = 'inferno', antialiased=True)\n",
    "       "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "c44a7e2d",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "/* global mpl */\n",
       "window.mpl = {};\n",
       "\n",
       "mpl.get_websocket_type = function () {\n",
       "    if (typeof WebSocket !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof MozWebSocket !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert(\n",
       "            'Your browser does not have WebSocket support. ' +\n",
       "                'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "                'Firefox 4 and 5 are also supported but you ' +\n",
       "                'have to enable WebSockets in about:config.'\n",
       "        );\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure = function (figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = this.ws.binaryType !== undefined;\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById('mpl-warnings');\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent =\n",
       "                'This browser does not support binary websocket messages. ' +\n",
       "                'Performance may be slow.';\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = document.createElement('div');\n",
       "    this.root.setAttribute('style', 'display: inline-block');\n",
       "    this._root_extra_style(this.root);\n",
       "\n",
       "    parent_element.appendChild(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen = function () {\n",
       "        fig.send_message('supports_binary', { value: fig.supports_binary });\n",
       "        fig.send_message('send_image_mode', {});\n",
       "        if (fig.ratio !== 1) {\n",
       "            fig.send_message('set_device_pixel_ratio', {\n",
       "                device_pixel_ratio: fig.ratio,\n",
       "            });\n",
       "        }\n",
       "        fig.send_message('refresh', {});\n",
       "    };\n",
       "\n",
       "    this.imageObj.onload = function () {\n",
       "        if (fig.image_mode === 'full') {\n",
       "            // Full images could contain transparency (where diff images\n",
       "            // almost always do), so we need to clear the canvas so that\n",
       "            // there is no ghosting.\n",
       "            fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "        }\n",
       "        fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "    };\n",
       "\n",
       "    this.imageObj.onunload = function () {\n",
       "        fig.ws.close();\n",
       "    };\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_header = function () {\n",
       "    var titlebar = document.createElement('div');\n",
       "    titlebar.classList =\n",
       "        'ui-dialog-titlebar ui-widget-header ui-corner-all ui-helper-clearfix';\n",
       "    var titletext = document.createElement('div');\n",
       "    titletext.classList = 'ui-dialog-title';\n",
       "    titletext.setAttribute(\n",
       "        'style',\n",
       "        'width: 100%; text-align: center; padding: 3px;'\n",
       "    );\n",
       "    titlebar.appendChild(titletext);\n",
       "    this.root.appendChild(titlebar);\n",
       "    this.header = titletext;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (_canvas_div) {};\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = (this.canvas_div = document.createElement('div'));\n",
       "    canvas_div.setAttribute(\n",
       "        'style',\n",
       "        'border: 1px solid #ddd;' +\n",
       "            'box-sizing: content-box;' +\n",
       "            'clear: both;' +\n",
       "            'min-height: 1px;' +\n",
       "            'min-width: 1px;' +\n",
       "            'outline: 0;' +\n",
       "            'overflow: hidden;' +\n",
       "            'position: relative;' +\n",
       "            'resize: both;'\n",
       "    );\n",
       "\n",
       "    function on_keyboard_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.key_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    canvas_div.addEventListener(\n",
       "        'keydown',\n",
       "        on_keyboard_event_closure('key_press')\n",
       "    );\n",
       "    canvas_div.addEventListener(\n",
       "        'keyup',\n",
       "        on_keyboard_event_closure('key_release')\n",
       "    );\n",
       "\n",
       "    this._canvas_extra_style(canvas_div);\n",
       "    this.root.appendChild(canvas_div);\n",
       "\n",
       "    var canvas = (this.canvas = document.createElement('canvas'));\n",
       "    canvas.classList.add('mpl-canvas');\n",
       "    canvas.setAttribute('style', 'box-sizing: content-box;');\n",
       "\n",
       "    this.context = canvas.getContext('2d');\n",
       "\n",
       "    var backingStore =\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        this.context.webkitBackingStorePixelRatio ||\n",
       "        this.context.mozBackingStorePixelRatio ||\n",
       "        this.context.msBackingStorePixelRatio ||\n",
       "        this.context.oBackingStorePixelRatio ||\n",
       "        this.context.backingStorePixelRatio ||\n",
       "        1;\n",
       "\n",
       "    this.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband_canvas = (this.rubberband_canvas = document.createElement(\n",
       "        'canvas'\n",
       "    ));\n",
       "    rubberband_canvas.setAttribute(\n",
       "        'style',\n",
       "        'box-sizing: content-box; position: absolute; left: 0; top: 0; z-index: 1;'\n",
       "    );\n",
       "\n",
       "    // Apply a ponyfill if ResizeObserver is not implemented by browser.\n",
       "    if (this.ResizeObserver === undefined) {\n",
       "        if (window.ResizeObserver !== undefined) {\n",
       "            this.ResizeObserver = window.ResizeObserver;\n",
       "        } else {\n",
       "            var obs = _JSXTOOLS_RESIZE_OBSERVER({});\n",
       "            this.ResizeObserver = obs.ResizeObserver;\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.resizeObserverInstance = new this.ResizeObserver(function (entries) {\n",
       "        var nentries = entries.length;\n",
       "        for (var i = 0; i < nentries; i++) {\n",
       "            var entry = entries[i];\n",
       "            var width, height;\n",
       "            if (entry.contentBoxSize) {\n",
       "                if (entry.contentBoxSize instanceof Array) {\n",
       "                    // Chrome 84 implements new version of spec.\n",
       "                    width = entry.contentBoxSize[0].inlineSize;\n",
       "                    height = entry.contentBoxSize[0].blockSize;\n",
       "                } else {\n",
       "                    // Firefox implements old version of spec.\n",
       "                    width = entry.contentBoxSize.inlineSize;\n",
       "                    height = entry.contentBoxSize.blockSize;\n",
       "                }\n",
       "            } else {\n",
       "                // Chrome <84 implements even older version of spec.\n",
       "                width = entry.contentRect.width;\n",
       "                height = entry.contentRect.height;\n",
       "            }\n",
       "\n",
       "            // Keep the size of the canvas and rubber band canvas in sync with\n",
       "            // the canvas container.\n",
       "            if (entry.devicePixelContentBoxSize) {\n",
       "                // Chrome 84 implements new version of spec.\n",
       "                canvas.setAttribute(\n",
       "                    'width',\n",
       "                    entry.devicePixelContentBoxSize[0].inlineSize\n",
       "                );\n",
       "                canvas.setAttribute(\n",
       "                    'height',\n",
       "                    entry.devicePixelContentBoxSize[0].blockSize\n",
       "                );\n",
       "            } else {\n",
       "                canvas.setAttribute('width', width * fig.ratio);\n",
       "                canvas.setAttribute('height', height * fig.ratio);\n",
       "            }\n",
       "            canvas.setAttribute(\n",
       "                'style',\n",
       "                'width: ' + width + 'px; height: ' + height + 'px;'\n",
       "            );\n",
       "\n",
       "            rubberband_canvas.setAttribute('width', width);\n",
       "            rubberband_canvas.setAttribute('height', height);\n",
       "\n",
       "            // And update the size in Python. We ignore the initial 0/0 size\n",
       "            // that occurs as the element is placed into the DOM, which should\n",
       "            // otherwise not happen due to the minimum size styling.\n",
       "            if (fig.ws.readyState == 1 && width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    this.resizeObserverInstance.observe(canvas_div);\n",
       "\n",
       "    function on_mouse_event_closure(name) {\n",
       "        return function (event) {\n",
       "            return fig.mouse_event(event, name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousedown',\n",
       "        on_mouse_event_closure('button_press')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseup',\n",
       "        on_mouse_event_closure('button_release')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'dblclick',\n",
       "        on_mouse_event_closure('dblclick')\n",
       "    );\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mousemove',\n",
       "        on_mouse_event_closure('motion_notify')\n",
       "    );\n",
       "\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseenter',\n",
       "        on_mouse_event_closure('figure_enter')\n",
       "    );\n",
       "    rubberband_canvas.addEventListener(\n",
       "        'mouseleave',\n",
       "        on_mouse_event_closure('figure_leave')\n",
       "    );\n",
       "\n",
       "    canvas_div.addEventListener('wheel', function (event) {\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        on_mouse_event_closure('scroll')(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.appendChild(canvas);\n",
       "    canvas_div.appendChild(rubberband_canvas);\n",
       "\n",
       "    this.rubberband_context = rubberband_canvas.getContext('2d');\n",
       "    this.rubberband_context.strokeStyle = '#000000';\n",
       "\n",
       "    this._resize_canvas = function (width, height, forward) {\n",
       "        if (forward) {\n",
       "            canvas_div.style.width = width + 'px';\n",
       "            canvas_div.style.height = height + 'px';\n",
       "        }\n",
       "    };\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    this.rubberband_canvas.addEventListener('contextmenu', function (_e) {\n",
       "        event.preventDefault();\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus() {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'mpl-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'mpl-button-group';\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'mpl-button-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        var button = (fig.buttons[name] = document.createElement('button'));\n",
       "        button.classList = 'mpl-widget';\n",
       "        button.setAttribute('role', 'button');\n",
       "        button.setAttribute('aria-disabled', 'false');\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "\n",
       "        var icon_img = document.createElement('img');\n",
       "        icon_img.src = '_images/' + image + '.png';\n",
       "        icon_img.srcset = '_images/' + image + '_large.png 2x';\n",
       "        icon_img.alt = tooltip;\n",
       "        button.appendChild(icon_img);\n",
       "\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    var fmt_picker = document.createElement('select');\n",
       "    fmt_picker.classList = 'mpl-widget';\n",
       "    toolbar.appendChild(fmt_picker);\n",
       "    this.format_dropdown = fmt_picker;\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = document.createElement('option');\n",
       "        option.selected = fmt === mpl.default_extension;\n",
       "        option.innerHTML = fmt;\n",
       "        fmt_picker.appendChild(option);\n",
       "    }\n",
       "\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.request_resize = function (x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', { width: x_pixels, height: y_pixels });\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_message = function (type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function () {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({ type: 'draw', figure_id: this.id }));\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function (fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] !== fig.canvas.width || size[1] !== fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1], msg['forward']);\n",
       "        fig.send_message('refresh', {});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function (fig, msg) {\n",
       "    var x0 = msg['x0'] / fig.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / fig.ratio;\n",
       "    var x1 = msg['x1'] / fig.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / fig.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0,\n",
       "        0,\n",
       "        fig.canvas.width / fig.ratio,\n",
       "        fig.canvas.height / fig.ratio\n",
       "    );\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function (fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function (fig, msg) {\n",
       "    fig.rubberband_canvas.style.cursor = msg['cursor'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_message = function (fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function (fig, _msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function (fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_history_buttons = function (fig, msg) {\n",
       "    for (var key in msg) {\n",
       "        if (!(key in fig.buttons)) {\n",
       "            continue;\n",
       "        }\n",
       "        fig.buttons[key].disabled = !msg[key];\n",
       "        fig.buttons[key].setAttribute('aria-disabled', !msg[key]);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_navigate_mode = function (fig, msg) {\n",
       "    if (msg['mode'] === 'PAN') {\n",
       "        fig.buttons['Pan'].classList.add('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    } else if (msg['mode'] === 'ZOOM') {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.add('active');\n",
       "    } else {\n",
       "        fig.buttons['Pan'].classList.remove('active');\n",
       "        fig.buttons['Zoom'].classList.remove('active');\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message('ack', {});\n",
       "};\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function (fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            var img = evt.data;\n",
       "            if (img.type !== 'image/png') {\n",
       "                /* FIXME: We get \"Resource interpreted as Image but\n",
       "                 * transferred with MIME type text/plain:\" errors on\n",
       "                 * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "                 * to be part of the websocket stream */\n",
       "                img.type = 'image/png';\n",
       "            }\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src\n",
       "                );\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                img\n",
       "            );\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        } else if (\n",
       "            typeof evt.data === 'string' &&\n",
       "            evt.data.slice(0, 21) === 'data:image/png;base64'\n",
       "        ) {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig['handle_' + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\n",
       "                \"No handler for the '\" + msg_type + \"' message type: \",\n",
       "                msg\n",
       "            );\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\n",
       "                    \"Exception inside the 'handler_\" + msg_type + \"' callback:\",\n",
       "                    e,\n",
       "                    e.stack,\n",
       "                    msg\n",
       "                );\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "};\n",
       "\n",
       "// from https://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function (e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e) {\n",
       "        e = window.event;\n",
       "    }\n",
       "    if (e.target) {\n",
       "        targ = e.target;\n",
       "    } else if (e.srcElement) {\n",
       "        targ = e.srcElement;\n",
       "    }\n",
       "    if (targ.nodeType === 3) {\n",
       "        // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "    }\n",
       "\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    var boundingRect = targ.getBoundingClientRect();\n",
       "    var x = e.pageX - (boundingRect.left + document.body.scrollLeft);\n",
       "    var y = e.pageY - (boundingRect.top + document.body.scrollTop);\n",
       "\n",
       "    return { x: x, y: y };\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * https://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys(original) {\n",
       "    return Object.keys(original).reduce(function (obj, key) {\n",
       "        if (typeof original[key] !== 'object') {\n",
       "            obj[key] = original[key];\n",
       "        }\n",
       "        return obj;\n",
       "    }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function (event, name) {\n",
       "    var canvas_pos = mpl.findpos(event);\n",
       "\n",
       "    if (name === 'button_press') {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * this.ratio;\n",
       "    var y = canvas_pos.y * this.ratio;\n",
       "\n",
       "    this.send_message(name, {\n",
       "        x: x,\n",
       "        y: y,\n",
       "        button: event.button,\n",
       "        step: event.step,\n",
       "        guiEvent: simpleKeys(event),\n",
       "    });\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (_event, _name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.key_event = function (event, name) {\n",
       "    // Prevent repeat events\n",
       "    if (name === 'key_press') {\n",
       "        if (event.key === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.key;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.key !== 'Control') {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    else if (event.altKey && event.key !== 'Alt') {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    else if (event.shiftKey && event.key !== 'Shift') {\n",
       "        value += 'shift+';\n",
       "    }\n",
       "\n",
       "    value += 'k' + event.key;\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, { key: value, guiEvent: simpleKeys(event) });\n",
       "    return false;\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function (name) {\n",
       "    if (name === 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message('toolbar_button', { name: name });\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function (tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "\n",
       "///////////////// REMAINING CONTENT GENERATED BY embed_js.py /////////////////\n",
       "// prettier-ignore\n",
       "var _JSXTOOLS_RESIZE_OBSERVER=function(A){var t,i=new WeakMap,n=new WeakMap,a=new WeakMap,r=new WeakMap,o=new Set;function s(e){if(!(this instanceof s))throw new TypeError(\"Constructor requires 'new' operator\");i.set(this,e)}function h(){throw new TypeError(\"Function is not a constructor\")}function c(e,t,i,n){e=0 in arguments?Number(arguments[0]):0,t=1 in arguments?Number(arguments[1]):0,i=2 in arguments?Number(arguments[2]):0,n=3 in arguments?Number(arguments[3]):0,this.right=(this.x=this.left=e)+(this.width=i),this.bottom=(this.y=this.top=t)+(this.height=n),Object.freeze(this)}function d(){t=requestAnimationFrame(d);var s=new WeakMap,p=new Set;o.forEach((function(t){r.get(t).forEach((function(i){var r=t instanceof window.SVGElement,o=a.get(t),d=r?0:parseFloat(o.paddingTop),f=r?0:parseFloat(o.paddingRight),l=r?0:parseFloat(o.paddingBottom),u=r?0:parseFloat(o.paddingLeft),g=r?0:parseFloat(o.borderTopWidth),m=r?0:parseFloat(o.borderRightWidth),w=r?0:parseFloat(o.borderBottomWidth),b=u+f,F=d+l,v=(r?0:parseFloat(o.borderLeftWidth))+m,W=g+w,y=r?0:t.offsetHeight-W-t.clientHeight,E=r?0:t.offsetWidth-v-t.clientWidth,R=b+v,z=F+W,M=r?t.width:parseFloat(o.width)-R-E,O=r?t.height:parseFloat(o.height)-z-y;if(n.has(t)){var k=n.get(t);if(k[0]===M&&k[1]===O)return}n.set(t,[M,O]);var S=Object.create(h.prototype);S.target=t,S.contentRect=new c(u,d,M,O),s.has(i)||(s.set(i,[]),p.add(i)),s.get(i).push(S)}))})),p.forEach((function(e){i.get(e).call(e,s.get(e),e)}))}return s.prototype.observe=function(i){if(i instanceof window.Element){r.has(i)||(r.set(i,new Set),o.add(i),a.set(i,window.getComputedStyle(i)));var n=r.get(i);n.has(this)||n.add(this),cancelAnimationFrame(t),t=requestAnimationFrame(d)}},s.prototype.unobserve=function(i){if(i instanceof window.Element&&r.has(i)){var n=r.get(i);n.has(this)&&(n.delete(this),n.size||(r.delete(i),o.delete(i))),n.size||r.delete(i),o.size||cancelAnimationFrame(t)}},A.DOMRectReadOnly=c,A.ResizeObserver=s,A.ResizeObserverEntry=h,A}; // eslint-disable-line\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Left button pans, Right button zooms\\nx/y fixes axis, CTRL fixes aspect\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\\nx/y fixes axis\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pgf\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";/* global mpl */\n",
       "\n",
       "var comm_websocket_adapter = function (comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.binaryType = comm.kernel.ws.binaryType;\n",
       "    ws.readyState = comm.kernel.ws.readyState;\n",
       "    function updateReadyState(_event) {\n",
       "        if (comm.kernel.ws) {\n",
       "            ws.readyState = comm.kernel.ws.readyState;\n",
       "        } else {\n",
       "            ws.readyState = 3; // Closed state.\n",
       "        }\n",
       "    }\n",
       "    comm.kernel.ws.addEventListener('open', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('close', updateReadyState);\n",
       "    comm.kernel.ws.addEventListener('error', updateReadyState);\n",
       "\n",
       "    ws.close = function () {\n",
       "        comm.close();\n",
       "    };\n",
       "    ws.send = function (m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function (msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        var data = msg['content']['data'];\n",
       "        if (data['blob'] !== undefined) {\n",
       "            data = {\n",
       "                data: new Blob(msg['buffers'], { type: data['blob'] }),\n",
       "            };\n",
       "        }\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(data);\n",
       "    });\n",
       "    return ws;\n",
       "};\n",
       "\n",
       "mpl.mpl_figure_comm = function (comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = document.getElementById(id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm);\n",
       "\n",
       "    function ondownload(figure, _format) {\n",
       "        window.open(figure.canvas.toDataURL());\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy, ondownload, element);\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element;\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error('Failed to find cell for figure', id, fig);\n",
       "        return;\n",
       "    }\n",
       "    fig.cell_info[0].output_area.element.on(\n",
       "        'cleared',\n",
       "        { fig: fig },\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function (fig, msg) {\n",
       "    var width = fig.canvas.width / fig.ratio;\n",
       "    fig.cell_info[0].output_area.element.off(\n",
       "        'cleared',\n",
       "        fig._remove_fig_handler\n",
       "    );\n",
       "    fig.resizeObserverInstance.unobserve(fig.canvas_div);\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable();\n",
       "    fig.parent_element.innerHTML =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "    fig.close_ws(fig, msg);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.close_ws = function (fig, msg) {\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function (_remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width / this.ratio;\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] =\n",
       "        '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function () {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message('ack', {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () {\n",
       "        fig.push_to_output();\n",
       "    }, 1000);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function () {\n",
       "    var fig = this;\n",
       "\n",
       "    var toolbar = document.createElement('div');\n",
       "    toolbar.classList = 'btn-toolbar';\n",
       "    this.root.appendChild(toolbar);\n",
       "\n",
       "    function on_click_closure(name) {\n",
       "        return function (_event) {\n",
       "            return fig.toolbar_button_onclick(name);\n",
       "        };\n",
       "    }\n",
       "\n",
       "    function on_mouseover_closure(tooltip) {\n",
       "        return function (event) {\n",
       "            if (!event.currentTarget.disabled) {\n",
       "                return fig.toolbar_button_onmouseover(tooltip);\n",
       "            }\n",
       "        };\n",
       "    }\n",
       "\n",
       "    fig.buttons = {};\n",
       "    var buttonGroup = document.createElement('div');\n",
       "    buttonGroup.classList = 'btn-group';\n",
       "    var button;\n",
       "    for (var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            /* Instead of a spacer, we start a new button group. */\n",
       "            if (buttonGroup.hasChildNodes()) {\n",
       "                toolbar.appendChild(buttonGroup);\n",
       "            }\n",
       "            buttonGroup = document.createElement('div');\n",
       "            buttonGroup.classList = 'btn-group';\n",
       "            continue;\n",
       "        }\n",
       "\n",
       "        button = fig.buttons[name] = document.createElement('button');\n",
       "        button.classList = 'btn btn-default';\n",
       "        button.href = '#';\n",
       "        button.title = name;\n",
       "        button.innerHTML = '<i class=\"fa ' + image + ' fa-lg\"></i>';\n",
       "        button.addEventListener('click', on_click_closure(method_name));\n",
       "        button.addEventListener('mouseover', on_mouseover_closure(tooltip));\n",
       "        buttonGroup.appendChild(button);\n",
       "    }\n",
       "\n",
       "    if (buttonGroup.hasChildNodes()) {\n",
       "        toolbar.appendChild(buttonGroup);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = document.createElement('span');\n",
       "    status_bar.classList = 'mpl-message pull-right';\n",
       "    toolbar.appendChild(status_bar);\n",
       "    this.message = status_bar;\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = document.createElement('div');\n",
       "    buttongrp.classList = 'btn-group inline pull-right';\n",
       "    button = document.createElement('button');\n",
       "    button.classList = 'btn btn-mini btn-primary';\n",
       "    button.href = '#';\n",
       "    button.title = 'Stop Interaction';\n",
       "    button.innerHTML = '<i class=\"fa fa-power-off icon-remove icon-large\"></i>';\n",
       "    button.addEventListener('click', function (_evt) {\n",
       "        fig.handle_close(fig, {});\n",
       "    });\n",
       "    button.addEventListener(\n",
       "        'mouseover',\n",
       "        on_mouseover_closure('Stop Interaction')\n",
       "    );\n",
       "    buttongrp.appendChild(button);\n",
       "    var titlebar = this.root.querySelector('.ui-dialog-titlebar');\n",
       "    titlebar.insertBefore(buttongrp, titlebar.firstChild);\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._remove_fig_handler = function (event) {\n",
       "    var fig = event.data.fig;\n",
       "    if (event.target !== this) {\n",
       "        // Ignore bubbled events from children.\n",
       "        return;\n",
       "    }\n",
       "    fig.close_ws(fig, {});\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function (el) {\n",
       "    el.style.boxSizing = 'content-box'; // override notebook setting of border-box.\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function (el) {\n",
       "    // this is important to make the div 'focusable\n",
       "    el.setAttribute('tabindex', 0);\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    } else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function (event, _name) {\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which === 13) {\n",
       "        this.canvas_div.blur();\n",
       "        // select the cell after this one\n",
       "        var index = IPython.notebook.find_cell_index(this.cell_info[0]);\n",
       "        IPython.notebook.select(index + 1);\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_save = function (fig, _msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "};\n",
       "\n",
       "mpl.find_output_cell = function (html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i = 0; i < ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code') {\n",
       "            for (var j = 0; j < cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] === html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "};\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel !== null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target(\n",
       "        'matplotlib',\n",
       "        mpl.mpl_figure_comm\n",
       "    );\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()                                     #Animation for 3D hard disks\n",
    "ax = fig.add_subplot(111, projection='3d')\n",
    "N=3\n",
    "sigma = 0.1\n",
    "delta = 0.2\n",
    "L = np.asarray(direct_disks_box3D(N, sigma))\n",
    "ani = animation.FuncAnimation(fig, animate, frames = 500, interval = 0.1)\n",
    "#ani.save('yourpath/mcmc3D.gif', writer = 'pillow', dpi = 100) "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "088f853c",
   "metadata": {},
   "source": [
    "-------------------------------------------------------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94b05c57",
   "metadata": {},
   "source": [
    "Increasing the density produces the packing of spheres."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}