Notebook demonstrating Tupper's Self-Referential Formula

tupper.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tuppers Self-referential Formula\n",
    "\n",
    "- http://mathworld.wolfram.com/TuppersSelf-ReferentialFormula.html\n",
    "- https://en.wikipedia.org/wiki/Tupper%27s_self-referential_formula\n",
    "\n",
    "via https://twitter.com/jhamrick/status/589127995677220864"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{1}{2} < \\left\\lfloor\\bmod\\left(\\left\\lfloor\\frac{y}{17}\\right\\rfloor 2 ^{-17 \\lfloor x\\rfloor - \\bmod(\\lfloor y\\rfloor, 17)}, 2\\right)\\right\\rfloor$$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Math\n",
    "formula = r'\\frac{1}{2} < \\left\\lfloor\\bmod\\left(\\left\\lfloor\\frac{y}{17}\\right\\rfloor 2 ^{-17 \\lfloor x\\rfloor - \\bmod(\\lfloor y\\rfloor, 17)}, 2\\right)\\right\\rfloor'\n",
    "Math(formula)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def Tupper():\n",
    "    \"\"\"\n",
    "    Implement Tupper's Formula in pure python\n",
    "    \n",
    "    Some re-arrangement is needed to avoid implicit casts to float\n",
    "    \"\"\"\n",
    "    # magic n copied from wikipedia, inline string processing and convert to int\n",
    "    n = int('960 939 379 918 958 884 971 672 962 127 852 754 715 004 339 660 129 306 651 505 519 271 702 802 395 266 424 689 642 842 174 350 718 121 267 153 782 770 623 355 993 237 280 874 144 307 891 325 963 941 337 723 487 857 735 749 823 926 629 715 517 173 716 995 165 232 890 538 221 612 403 238 855 866 184 013 235 585 136 048 828 693 337 902 491 454 229 288 667 081 096 184 496 091 705 183 454 067 827 731 551 705 405 381 627 380 967 602 565 625 016 981 482 083 418 783 163 849 115 590 225 610 003 652 351 370 343 874 461 848 378 737 238 198 224 849 863 465 033 159 410 054 974 700 593 138 339 226 497 249 461 751 545 728 366 702 369 745 461 014 655 997 933 798 537 483 143 786 841 806 593 422 227 898 388 722 980 000 748 404 719'.replace(' ', ''))\n",
    "    # output array\n",
    "    out = []\n",
    "    # loop over \n",
    "    for _y in range(17):\n",
    "        tmp = []\n",
    "        out.append(tmp)\n",
    "        for x in range(106):\n",
    "            y = n + _y\n",
    "            a = y // 17\n",
    "            y_mod = y % 17\n",
    "            xp = -(-17 * x - y_mod)\n",
    "            pix_val = 1 < 2*(((a // (2 ** xp)) % 2) // 1)\n",
    "            tmp.append(pix_val)\n",
    "\n",
    "    return out\n",
    "\n",
    "out = Tupper()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "def Tupper_np():\n",
    "    \"\"\"\n",
    "    Implemented using numpy.  Some slight rearrengements to keep everything as integers\n",
    "    \n",
    "    \n",
    "    \"\"\"\n",
    "    n = int('960 939 379 918 958 884 971 672 962 127 852 754 715 004 339 660 129 306 651 505 519 271 702 802 395 266 424 689 642 842 174 350 718 121 267 153 782 770 623 355 993 237 280 874 144 307 891 325 963 941 337 723 487 857 735 749 823 926 629 715 517 173 716 995 165 232 890 538 221 612 403 238 855 866 184 013 235 585 136 048 828 693 337 902 491 454 229 288 667 081 096 184 496 091 705 183 454 067 827 731 551 705 405 381 627 380 967 602 565 625 016 981 482 083 418 783 163 849 115 590 225 610 003 652 351 370 343 874 461 848 378 737 238 198 224 849 863 465 033 159 410 054 974 700 593 138 339 226 497 249 461 751 545 728 366 702 369 745 461 014 655 997 933 798 537 483 143 786 841 806 593 422 227 898 388 722 980 000 748 404 719'.replace(' ', ''))\n",
    "    x, _y = np.meshgrid(np.arange(106), np.arange(17))\n",
    "    y = _y + n\n",
    "    out = 1 < 2 * np.mod((y // 17) // (2 ** (17 * x + np.mod(y, 17))), 2)\n",
    "    \n",
    "    return out\n",
    "\n",
    "out2 = Tupper_np()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\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('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",
       "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 = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(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",
       "            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",
       "            fig.waiting = false;\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        this.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 = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width);\n",
       "        canvas.attr('height', height);\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\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 nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\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",
       "\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",
       "\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]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'];\n",
       "    var y0 = fig.canvas.height - msg['y0'];\n",
       "    var x1 = msg['x1'];\n",
       "    var y1 = fig.canvas.height - msg['y1'];\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, 0, fig.canvas.width, fig.canvas.height);\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",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = 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.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",
       "            /* 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",
       "            evt.data.type = \"image/png\";\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",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\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(\"No handler for the '\" + msg_type + \"' message type: \", msg);\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(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://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",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\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",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x;\n",
       "    var y = canvas_pos.y;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step});\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",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value});\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",
       "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\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";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.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",
       "        // Pass the mpl event to the overriden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['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 = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\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.get(0);\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",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\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).html('<img src=\"' + dataURL + '\">');\n",
       "    fig.send_message('closing', {});\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 dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\">';\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 () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\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) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-danger\" href=\"#\" title=\"Close figure\"><i class=\"fa fa-times icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Close figure', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('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",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\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('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7faf01051a58>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "import matplotlib\n",
    "matplotlib.rcParams['text.usetex'] = True\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(2, 1)\n",
    "\n",
    "ax1.imshow(1 - np.fliplr(out), interpolation='nearest', cmap='gray')\n",
    "ax1.set_title('pure python')\n",
    "\n",
    "ax2.imshow(1 - np.fliplr(out2), interpolation='nearest', cmap='gray')\n",
    "ax2.set_title('numpy')\n",
    "\n",
    "fig.suptitle('$' + formula + '$', fontsize=24)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
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