Mandelbrot Set.ipynb

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   "cell_type": "markdown",
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   "source": [
    "[Oregon Curriculum Network](http://www.4dsolutions.net/ocn) <br />\n",
    "[Discovering Math with Python](Introduction.ipynb)\n",
    "\n",
    "# The Mandelbrot Set\n",
    "\n",
    "Welcome to our Jupyter Notebook about the Mandelbrot Set.  We will be taking the complex number c at each point, and adding it to z \\* z, where z starts out 0.  z = z * z + c.  Do that over and over, up to 80 times in this case.  It's a survivor's game in that most points subjected to this algorithm spiral out of the grid after a few iterations.  Others hang in there.  At the end, we image how all the points did i.e. we colorize by how many iterations each survived, before having too big a magnitude.\n",
    "\n",
    "You may not remember how complex numbers multiply:  imagined as arrows pointing from the origin, we multiply the arrow lengths and add their angles.  Adding complex numbers is like adding two vectors, tip to tail.\n",
    "\n",
    "What are \"vectorized\" operations?  That's where entire data structures act like individual objects.  Every element is affected, potentially, but without our needing to write looping code to visit every cell individually.  Lets start with a simple example..."
   ]
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   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "r1 = np.array([[1,2,3],[4,5,6]])\n",
    "r2 = np.ones((2,3))  # the (2,3) is the \"shape\" of the array we want, 2 rows, 3 columns\n",
    "r1"
   ]
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  {
   "cell_type": "code",
   "execution_count": 2,
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    {
     "data": {
      "text/plain": [
       "array([[ 1.,  1.,  1.],\n",
       "       [ 1.,  1.,  1.]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Both these arrays have the same shape.  We may add them...."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.,  3.,  4.],\n",
       "       [ 5.,  6.,  7.]])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r1 + r2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  2.,   5.,  10.],\n",
       "       [ 17.,  26.,  37.]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "r1 ** 2 + r2  # we may also multipy r1 by itself (not matrix multiplication) and add r2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function below is all about vectorizing.  Both z and output are 1000 x 1000 arrays! "
   ]
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  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
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   "source": [
    "def mandelbrot_numpy(c, maxiter):\n",
    "    output = np.zeros(c.shape)\n",
    "    z = np.zeros(c.shape, np.complex64)\n",
    "    for it in range(maxiter):\n",
    "        # not done are the numbers that haven't spiralled away by this many iterations\n",
    "        notdone = np.less(z.real*z.real + z.imag*z.imag, 4.0) # magnitude test!\n",
    "        output[notdone] = it  # lets keep track of how many iterations in output\n",
    "        z[notdone] = z[notdone]**2 + c[notdone]  # on to the next iteration!\n",
    "    output[output == maxiter-1] = 0  # these made it to the end\n",
    "    return output"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets look at a smaller slice of the complex plane to being with.  This rectangle of complex numbers starts from (-1, -1j) and ends at (1, 1j), dividing both the real and imaginary axes into three intervals marked by four tick marks."
   ]
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   "cell_type": "code",
   "execution_count": 6,
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.-1.j        ],\n",
       "       [-0.-0.33333334j],\n",
       "       [ 0.+0.33333334j],\n",
       "       [ 0.+1.j        ]], dtype=complex64)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "r1 = np.linspace(-1, 1, 4, dtype=np.float32)\n",
    "r2 = np.linspace(-1, 1, 4, dtype=np.float32)\n",
    "r2_T = (r2 * 1j).reshape(4,1)\n",
    "r2_T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By reshaping r2 into r2_T, we make it a vertical column.  Then we add.  The result is a 4x4 matrix, from (-1, -1) upper left, to (1, 1) lower right."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.00000000-1.j        , -0.33333334-1.j        ,\n",
       "         0.33333334-1.j        ,  1.00000000-1.j        ],\n",
       "       [-1.00000000-0.33333334j, -0.33333334-0.33333334j,\n",
       "         0.33333334-0.33333334j,  1.00000000-0.33333334j],\n",
       "       [-1.00000000+0.33333334j, -0.33333334+0.33333334j,\n",
       "         0.33333334+0.33333334j,  1.00000000+0.33333334j],\n",
       "       [-1.00000000+1.j        , -0.33333334+1.j        ,\n",
       "         0.33333334+1.j        ,  1.00000000+1.j        ]], dtype=complex64)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r1 + r2_T"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice how we were able to add rectangular arrays r1 and r2_T in one line, with no loops."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def mandelbrot_set(xmin,xmax,ymin,ymax,width,height,maxiter):\n",
    "    r1 = np.linspace(xmin, xmax, width, dtype=np.float32)\n",
    "    r2 = np.linspace(ymin, ymax, height, dtype=np.float32)\n",
    "    c = r1 + (r2 * 1j).reshape(width,1)  # x row + each y column\n",
    "    n3 = mandelbrot_numpy(c, maxiter)\n",
    "    return (r1,r2,n3) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Python standard library has a timeit module.  Jupyter Notebooks add a layer of %magic by giving us the %timeit directive.  We're able to see how long the operation takes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 loop, best of 3: 1.32 s per loop\n"
     ]
    }
   ],
   "source": [
    "%timeit mandelbrot_set(-2.0,0.5,-1.25,1.25,1000,1000,80)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "r1, r2, result = mandelbrot_set(-2.0,0.5,-1.25,1.25,1000,1000,80)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now have the array we want to plot in result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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       "        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'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.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, 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",
       "            fig.waiting = false;\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",
       "            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(\"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",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://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",
       "    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",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\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",
       "                             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",
       "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",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\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).html('<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/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<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 () { 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 = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\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",
       "        // 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",
       "\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"
    }
   ],
   "source": [
    "%matplotlib notebook\n",
    "import matplotlib.pyplot as plt\n",
    "fig, ax = plt.subplots()\n",
    "im = ax.imshow(result, extent=[-2.0,0.5,-1.25,1.25])\n",
    "fig.colorbar(im)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice how some of these points made almost to the maximum number of iterations before hitting a cut-off.  Those that never hit a cut-off get to be 0 and are considered to be members of the Mandelbrot Set.\n",
    "\n",
    "For further reading:\n",
    "\n",
    "* [How To Quickly Compute The Mandelbrot Set In Python by Jean Francois Puget](https://www.ibm.com/developerworks/community/blogs/jfp/entry/How_To_Compute_Mandelbrodt_Set_Quickly?lang=en)\n",
    "\n",
    "* [CS-friendly math course (thread on math-teach @ Math Forum)](http://mathforum.org/kb/thread.jspa?threadID=2870943)\n",
    " \n",
    "Back to Chapter 11: [Quaternions](Quaternions.ipynb) <br />\n",
    "[Introduction](Introduction.ipynb)"
   ]
  }
 ],
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   "codemirror_mode": {
    "name": "ipython",
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   "file_extension": ".py",
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   "name": "python",
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   "pygments_lexer": "ipython3",
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