estimatingPi.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Estimating *$\\pi$* using the Monte Carlo Method"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-------------------\n",
    "| Explanation |    |\n",
    "|:-----------|:-------:|\n",
    "|Assume we have a circle of radius *r*. This circle can be inscribed inside a square of width *2r*. Pi can then be estimated by randomly selecting an *x* and *y* point inside the square and looking at the number of points that land inside and outside the circle <br><br> $Area_c = \\pi r^2$ <br> $Area_s = (2r)^2 = 4r^2$ <br> $\\frac{Area_c}{Area_s} = \\frac{\\pi r^2}{4r^2} = \\frac{\\pi}{4}$ <br> $\\pi ≈ \\frac{4 Area_c}{Area_s}$ <br><br> This means that computing the ratio of the areas and multiplying by 4 should approximate $\\pi$|<img src=\"https://www.101computing.net/wp/wp-content/uploads/estimating-pi-monte-carlo-method.png\" alt=\"pi_monte_carlo\" style=\"width: 500px;\"/>|\n",
    "Can also think of as shown below:\n",
    "<img src=\"https://d138zd1ktt9iqe.cloudfront.net/media/seo_landing_files/derivation-of-area-of-a-circle-2-1615860096.png\" alt=\"pi_derivation\" style=\"width: 500px;\"/>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from ipywidgets import IntProgress\n",
    "from IPython.display import display\n",
    "%matplotlib notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
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       "\n",
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       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
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       "\n",
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       "    var cursor = msg['cursor'];\n",
       "    switch (cursor) {\n",
       "        case 0:\n",
       "            cursor = 'pointer';\n",
       "            break;\n",
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       "            cursor = 'default';\n",
       "            break;\n",
       "        case 2:\n",
       "            cursor = 'crosshair';\n",
       "            break;\n",
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       "            break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
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       "\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",
       "            /* 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",
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       "                );\n",
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       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data\n",
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       "            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 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",
       "    }\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",
       " * 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",
       "        }\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.which === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.which;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which !== 17) {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    if (event.altKey && event.which !== 18) {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    if (event.shiftKey && event.which !== 16) {\n",
       "        value += 'shift+';\n",
       "    }\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, 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\", \"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, CTRL fixes aspect\", \"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\";/* 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.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 overridden (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 = 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.one(\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",
       "\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",
       "    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",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager) {\n",
       "        manager = IPython.keyboard_manager;\n",
       "    }\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",
       "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"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Points inside circle: 78264\n",
      "Points outside circle: 21736\n",
      "Estimate for Pi: 3.13056\n"
     ]
    }
   ],
   "source": [
    "NUMBER_OF_SAMPLES = 10**5\n",
    "TIMES_TO_REDRAW_PLOT = 50\n",
    "\n",
    "_REDRAW_EVERY_X = NUMBER_OF_SAMPLES/TIMES_TO_REDRAW_PLOT\n",
    "\n",
    "inside_circle, outside_circle = [], []  # list of x,y points\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "def plot_animate():\n",
    "    has_enough_points = len(inside_circle) > 0 and len(outside_circle) > 0\n",
    "    if has_enough_points:\n",
    "        # only try to plot if we have enouguh items in our list\n",
    "        ax.clear()\n",
    "        \n",
    "        _inside_x, _inside_y = zip(*inside_circle)\n",
    "        _outside_x, _outside_y = zip(*outside_circle)\n",
    "        ax.plot(_inside_x, _inside_y, marker='o', markersize=1, color='r',linestyle = 'None')\n",
    "        ax.plot(_outside_x, _outside_y, marker='o', markersize=1, color='b',linestyle = 'None')\n",
    "\n",
    "        fig.canvas.draw()\n",
    "\n",
    "# Will loop through randomly genarated x and y points centered at zero ranging from -1 to 1. \n",
    "# Distance will be calculated and x and y points added to a list for plotting\n",
    "for i in range(NUMBER_OF_SAMPLES):\n",
    "    x = -1 + 2*random.random()\n",
    "    y = -1 + 2*random.random()\n",
    "    r = math.sqrt(x**2 + y**2)\n",
    "    # NOTE: numpy append() and concatenate() use append(). Untested\n",
    "    inside_circle.append([x,y]) if (r<1) else outside_circle.append([x,y])\n",
    "    if not (i % _REDRAW_EVERY_X): plot_animate()\n",
    "    \n",
    "    \n",
    "# Count number of points inside circle and outside circle (but inside square)\n",
    "_inside, _outside = len(inside_circle), len(outside_circle)\n",
    "print(\"Points inside circle: {}\".format(_inside))   \n",
    "print(\"Points outside circle: {}\".format(_outside))\n",
    "print(\"Estimate for Pi: {}\".format(4*_inside/(_inside+_outside)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculate how good the approximation gets as the number of samples increases"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ad5aff9071024090bd91e3f9f537afb8",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "IntProgress(value=1, max=1000, min=1)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Simulating 1000 tries...\n"
     ]
    },
    {
     "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_dpi_ratio', { dpi_ratio: fig.ratio });\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",
       "    if (this.ratio !== 1) {\n",
       "        fig.send_message('set_dpi_ratio', { dpi_ratio: this.ratio });\n",
       "    }\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",
       "    var resizeObserver = new 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 (width != 0 && height != 0) {\n",
       "                fig.request_resize(width, height);\n",
       "            }\n",
       "        }\n",
       "    });\n",
       "    resizeObserver.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",
       "    // 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",
       "    var cursor = msg['cursor'];\n",
       "    switch (cursor) {\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.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",
       "            /* 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",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data\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 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",
       "    }\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",
       " * 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",
       "        }\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.which === this._key) {\n",
       "            return;\n",
       "        } else {\n",
       "            this._key = event.which;\n",
       "        }\n",
       "    }\n",
       "    if (name === 'key_release') {\n",
       "        this._key = null;\n",
       "    }\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which !== 17) {\n",
       "        value += 'ctrl+';\n",
       "    }\n",
       "    if (event.altKey && event.which !== 18) {\n",
       "        value += 'alt+';\n",
       "    }\n",
       "    if (event.shiftKey && event.which !== 16) {\n",
       "        value += 'shift+';\n",
       "    }\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, 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\", \"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, CTRL fixes aspect\", \"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\";/* 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.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 overridden (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 = 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.one(\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",
       "\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",
       "    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",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager) {\n",
       "        manager = IPython.keyboard_manager;\n",
       "    }\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",
       "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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7qoxHpnVll0Hdsnx48drT0RbnCEdz+wYaPTw0cO1YqeltJSObTrK+e3Pl17n9pLyD8ulorJCzGMfc4yZ/J6Xf16wwmXahMlVUXxvvUYjGHDKosTHgI1/arws2bmk5reAM187aVD4WH7OrujM88bS7aXy4WcfBknfvMhkXvRy+Yzw5NWTa54nm3N3aN1BHhv6mNy+6nY5Un2kZgTNcq+5l5I3SqTVGa3k82Ofi/nbk8OelJ9v/3mwFDxnwJxgxm0+62yWxs02e8VsefDmB+stw+YijYzxPb/jefnos48CwzWJxFS7474+Tn6w+Qdyc6+bGzQ7Y8Zd2ncJJieZZeG617zkS5cEf3r343eDc5tl40e+/YgsfWNpULFO7jNZHvnNI1L6h9IGl9TN5CO/TX7AY/DFg+U/Bv5HzX2aRNl3cd9aDDPXN0nv7DZnB4nvUNUhufar10r3s7uHSnq58ExqG01yDXMvmWf1v9/ze+nTpU/NykTYc5qvlDWPSRr6Ktlcz20mvrc+c6vktcqT/t36ixyX4DvjzUqL2RpbbWnoGpn3KnK9fqZdmzPaiJlQnmo7I8vs604EjPkfOXZE6p6jsWOyr2PaFZxVUKtq12jERz535eazPRWwgqapgP/Q7g81vwVsXpAyFXDGlMIEZ93uXPPkNcFPGRoj3PrdrcELQOblLGPGjw973Np7YxLX/fi6YIm5oerWVGzm+ap5tmt+MMJsp/qd41NdTBM4DZ3LJKbvrfmePHbjY/We95r7mFA6Qbb/efspl4KNud7Q/YZgufvdj97N6Rl13SrbMDq77dlyZZcrgwp94d8ubHRZz/T5u6u+G6wG/N8n/yfvffKefFb92SnHxfxG9Ooxq+WNijeCxwpmmTu7IjEHZpJ89n8bTUVRdVgF5KmBL41kdyfz7kLFpxVijNZUexmjMBPL7ElZQ0aRMQCzWmOYm0c9971wX1BdmkckpzKdi86+SD4+/HGNYZo+5Wo8pu2BqgPBi4i2zTzKqWuQ5jpntTkr6KO0EPlKx68Ej2WWvLZEfvnOLwPzrnXfLdsEj4HMMebdilNNVG19iWp/9gulGo1gwFGNTETn/drXviYvv/xyqLO/9NJLcs0119Q6h3kG+NRrT8nt37g9WOb1tU1dN1V+/MaPZeLXJ8qCby+Q2Rtny4KXF8hVna+Skr8rafRapk8Dlg6QPZ/uCareJcOWyJxfz5HXPngt6J4J8BfGvCCXn395qO42xCPUCRs5+NWKV2XaC9Pkk88+kT9+/MegpZlEXNzpYnlsyGM192LaDX5msHz6+adBm3Z57aTPBX1k867NwRvadTdTTZvEmn0OzT0Y5v/yq3+Rsj+WyefyeZDw6lYoxgzMM+66SbhNizZBUg0qi6z/Pqv1WUFXMlXHuWeeK8N6DpP7+t5n1ZpNl4bTnWV3Bs+wjUbMW/anMgfz+OHScy8NXtQzk82B3QfK/QPut/bB9D2sRjL9NKsdmf4Zk81ewWlovGzVoXm3oFXLVsF5bG01emjsmLYt29ZM1syqj1ndMpvhbNh+f8D3c2KbfQ0zjg/85gExvP7q/L+S2X1n15wjs+93e34nn33+mew7XH+SkX2uYFLRuqPsr9rf8FJ4A/saO6buuc2jtex402jkyiuvlPLyct9Dc9rO1+wqYJM4wm4LFiyQwsLC2qe5TkTMP/PpoF+FvULW8R1ExHzS5RURMe9Jmf9/i4h0FZHfiMj6Rq51o4j0Obn/dyKy9uTxN4hINxFZJSI7wve1QR7hT9v4GQyHqyUwLHnpJJu6R1wgIn8rIhUisulkm78QkeEiYt5n62Sc2axPm4dypziH8j4CJvcVnhi7nSJimHc8yT9zTjMPOEN5AXOYeXpgzmH+/T8R2X+Shdlnrmc+Gdb65D/T9g8n919xUj+GYRsRaRmiD5lH7kabK09yNacz5zbX+ZOI9Be567K75NF1j5640Dsn/iZvnIyZvByub+7D1k/zcnpmbmUKzAMisllErj3JPjv0zTXNORvaMvdUN1WYc7Y6eZx5PzH7HUWzz1zfrOjaUky1yF1d7pJH5z56gsP5IlKWxS4HHE2xiSaP9OrVCwNOkxgiM+C6RhkllKEicqWIZEy1oWsZ85lwMiF8IiKL/RpM9iU1gRMlniScu0EmRiPGGC862cNfnpwIFZiy5+RkwOzKJHLz35mPUJuJQmbLb+QOjdEaAziVuZj35xoyPHNNYzyNGYg5pznWGI+ZONQ1RHPujCmZdsasGppkZP5mTMtmVtm3as5tXo7PHGOON3zMdXdlTbJyEUD2WJh7Mfdv7s82GTNxZT4BuC6cYRIz9QdJwwQDzkXsCWqTtiXohtDdu/FeWfjywgaXoc0y0/zfzZefbv+pVByqCJYVn7v1udDLzI0NoWbpKEGSiKQrUTHJLCP+ZudvgvE1zylP9dKOWZo3S+tmGXH3p7vrPTs3S+Fm2TPX5U6zrDn7f2bLg9c9GDCbun6qHDx8MDh3mGeLmSX2xgaiTV4bKR5SLN/q/q1Ixut0nzQqfZzu+/B5PQ0TlqB9jsBpOJePh/YNvSzQ2A8x+L4t8/LJyGdHBi9nmZexOnfoXPMCidmX+bywuW6uL2uF6aPm5Ykw10vDsaeTSfbHuj469JG0PKNlg29sm5fYjD7MR1HM27dFA4pCvc2bGYfMm+zmJaDMZ6UzLwuZz373/nJv2bZ7m5zb4dzg+a3525Q+U+TJbU82+MJdGsY3bB9Ppz7C9vV0Ha9h4iOfn677a+g6ze4ZsI8Ba0govr+EwyaKzEeLzAtfpioyL1TVfSGloEOBbJ201UuSbaw/msCx3V/a98Ok9gjCAx62mNZoxEc+t/Uryv0YsIKuRiiKyzR6SPavJmU+s5v9Fqf5DOoL33nhtHwzThJ4+OYb9nwwwXCYtLpFkSZmMGA3xrG39jFgDX0XtI8P6LvAMRX3VU9cFXwJhdnMs17zWd8rLrgi+AEE2+dXXa5la6sJHNs5074fJhgwBuwWxZqY8ZHP3Xrpt3ViK+CBAwfKBx98ELxk0rNnT3nqqaekY0fzOY4vto0bN8qUKVOkqqpK+vfvL8XFxZKX1/hnGnwMWF2hnM7nv9n3b579Df/J8MCEzbNe82UN5ss0fH4RSC5y0wROLudNcxuYYMAYsFsEa2LGRz5366Xf1ok14P3798tZZ534AoJp06YF/z1nzhc/QFBdXS09evSQ1atXS+/evWXUqFEyZMgQmThxYqOEfAxYQxWw+faoOMzvdD97bgiuJnD8yjh5Z4MJBowBu8WlJmZ85HO3XvptnVgDztzmsWPH5O6775bOnTvXMuAtW7bIzJkzZdMm8w0LIuvWrZOFCxcGhtzY5mPANELxO2zJOhs86o8HTDBgDNgtT2lixkc+d+ul39aJNuDhw4cHX2FnIK9du1batz/xVW1mW7FihZSWlkpJyYlfIdq+fbuMGTNGtm3bFrkBZ34NKeyXsvsdyvjOpgmc+Hp7eq4MEwwYA3aLNU3MYMBujJ1bm6Xm++67T84555yg4s024JUrV8rSpUuDP5nvAx07dmw9A160aJGYf5mtoqJCli9f7tyP7AOefOdJeWbvMzK+6/jgX3PfKisrJT+/sa9nan6EYFJ7zOEBD1sW0GjEfCUw3wVtIxty/1tvvSUjR46UN998s+ZMW7dulRkzZtQsQa9fv17MV5mdjiXozK8hxfHMNyTKSA7XzFwj6UiCTgoTKmAqYLeA1MQMFbAb45xaHzhwQMxsyDz3NdsDDzwgr7/+ujzzzDM1x5vK2LwdbQzXDMLo0aNl0KBBsbyEldNNNeFGmsBpwjiCW4MJBowBu0W5JmYwYDfGObXeuXOnjBgxQg4fPhz87Jn5/mZT3Zq/FxUVSVmZ+ekQkQ0bNsjUqVNj/xhSTjfVhBtpAqcJ48CAGxhcNMKExBbzGo1gwDaqCdvvY8A0QkkYBq/dgUd9nDDBcKiA3dKMJmZ85HO3Xvptnei3oP3e6omz+RgwjVCiuJeknBMeGLBNi2iECUkUGvGRz239inI/BqygSzIhmdhkg0bQCBWwLUrCawQDdmMce2sfA0ZyDR84sQsh4g6gETSCAbsFmSZmfORzt176bU0FrOCpEYriMqk5BB4sQdvEikaYkEShEQzYRjVh+30MGMmEZGKTNRpBI1TAtigJrxEf+dytl35bUwEreJJcwweOAnuqDkEjaAQDdgtZTcxgwG6MY2/tY8A0Qon9xiPsADxYgrbJC40wIYlCIz7yua1fUe6nAlbQJZmQTGyyQSNohArYFiXhNYIBuzGOvbWPASO5hg+c2IUQcQfQCBrBgN2CTBMzPvK5Wy/9tqYCVvDUCEVxmdQcAg+WoG1iRSNMSKLQCAZso5qw/T4GjGRCMrHJGo2gESpgW5SE14iPfO7WS7+tqYAVPEmu4QNHgT1Vh6ARNIIBu4WsJmYwYDfGsbf2MWAaocR+4xF2AB4sQdvkhUaYkEShER/53NavKPdTASvokkxIJjbZoBE0QgVsi5LwGsGA3RjH3trHgJFcwwdO7EKIuANoBI1gwG5BpokZH/ncrZd+W1MBK3hqhKK4TGoOgQdL0DaxohEmJFFoBAO2UU3Yfh8DRjIhmdhkjUbQCBWwLUrCa8RHPnfrpd/WVMAKniTX8IGjwJ6qQ9AIGsGA3UJWEzMYsBvj2Fv7GLBny56V7e22y51X3CldOnSJ/Z7i7oAmcOLuc9TXhwkGjAG7RZkmZnzkc7de+m1NBazgOf6p8bJk5xKZO2CuzLlujuIMTesQTeA0LQL17wYmGDAG7BblmpjBgN0Yx97ax4CZCvgP7f4gk66YRAUsIprAiV0IEXcAJhgwBuwWZJqY8ZHP3XrptzUVsIKnRiiKy6TmEHhQAdvEikaYkEShEQzYRjVh+30MGMmEZGKTNRpBI1TAtigJrxEf+dytl35bUwEreJJcwweOAnuqDkEjaAQDdgtZTcxgwG6MY2/tY8A0Qon9xiPsADxYgrbJC40wIYlCIz7yua1fUe6nAlbQJZmQTGyyQSNohArYFiXhNYIBuzGOvbWPASO5hg+c2IUQcQfQCBrBgN2CTBMzPvK5Wy/9tk5kBbxz506ZMGGC7NmzR1q2bCk33XST3H///fXuvFu3bpKfny+tWrUK9i1btkzMgDS2+RgwjVD8DluyzgYPlqBtikQjTEii0IiPfG7rV5T7E2nA77//vuzevVv69OkjVVVVMnDgQJk+fboMHz68FgtjwJs3b5aCgoKcGfkYMJIJycQmODSCRqiAbVESXiM+8rlbL/22TqQB173FwsJC6dmzp5j/zd4wYL9i0J4Ns6ECtmkHjYQ3GxvjtO/XaAQDjnjU9+3bJ5dffrmsX79eevXqVc+AO3XqJMeOHZNhw4bJ3LlzJS8vjyXoiMek7uk1gXOau3jaLwcTDIcK2C3sNDGDAbsxdmp95MgRGTx4cLD0fM8999Q7dteuXcHy88GDB2XcuHHSt29fmTVrVq12ixYtEvMvs1VUVMjy5cud+lG3cWVlZfDsme0EAXjUVwJMajOBBzxs+VKjEbMqWl5ebjt1Yvcndgm6urpabr31Vunevbs89NBDVoBr1qyRxYsXS2lpKRWwlZbfBpqZq98eJO9sMKECpgJ2i0tNzFABuzHOufUdd9whx48fD0y1RYsW9Y4zsyVj0h07dpSjR4/KpEmTpGvXrjJv3jwMOGfKfhpqAsfPlZN7FphgwBiwW3xqYgYDdmOcU+sXX3xRrr32Wrn00kuDjyGZ7fbbbw+WmIuKiqSsrEx27NghI0aMCJ7/GiPu16+fzJ8/X9q2bYsB50TZXyNN4Pi7ejLPBBMMGAN2i01NzGDAboxjb+1jwDRCif3GI+wAPOrDhQkGjAG7JR1NzPjI52699Ns6sc+A/d7mF2fzMWAaoUR1P0k4LzwwYJsO0QgTkig04iOf2/oV5X4MWEGXZEIysckGjaARKmBblITXCAbsxjj21j4GjOQaPnBiF0LEHUAjaAQDdgsyTcz4yOduvfTbmgpYwVMjFMVlUnPvMqcGAAAgAElEQVQIPFiCtokVjTAhiUIjGLCNasL2+xgwkgnJxCZrNIJGqIBtURJeIz7yuVsv/bamAlbwJLmGDxwF9lQdgkbQCAbsFrKamMGA3RjH3trHgGmEEvuNR9gBeLAEbZMXGmFCEoVGfORzW7+i3E8FrKBLMiGZ2GSDRtAIFbAtSsJrBAN2Yxx7ax8DRnINHzixCyHiDqARNIIBuwWZJmZ85HO3XvptTQWs4KkRiuIyqTkEHixB28SKRpiQRKERDNhGNWH7fQwYyYRkYpM1GkEjVMC2KAmvER/53K2XfltTASt4klzDB44Ce6oOQSNoBAN2C1lNzGDAboxjb+1jwDRCif3GI+wAPFiCtskLjTAhiUIjPvK5rV9R7qcCVtAlmZBMbLJBI2iECtgWJeE1ggG7MY69tY8BI7mGD5zYhRBxB9AIGsGA3YJMEzM+8rlbL/22pgJW8NQIRXGZ1BwCD5agbWJFI0xIotAIBmyjmrD9PgaMZEIysckajaARKmBblITXiI987tZLv62pgBU8Sa7hA0eBPVWHoBE0ggG7hawmZjBgN8axt/YxYBqhxH7jEXYAHixB2+SFRpiQRKERH/nc1q8o91MBK+iSTEgmNtmgETRCBWyLkvAawYDdGMfe2seAkVzDB07sQoi4A2gEjWDAbkGmiRkf+dytl35bUwEreGqEorhMag6BB0vQNrGiESYkUWgEA7ZRTdh+HwNGMiGZ2GSNRtAIFbAtSsJrxEc+d+ul39ZUwAqeJNfwgaPAnqpD0AgawYDdQlYTMxiwG+PYW/sYMI1QYr/xCDsAD5agbfJCI0xIotCIj3xu61eU+6mAFXRJJiQTm2zQCBqhArZFSXiNYMBujHNqvXPnTpkwYYLs2bNHWrZsKTfddJPcf//99Y7duHGjTJkyRaqqqqR///5SXFwseXl5jV7Dx4CRXMMHTk5CSHEjNIJGMGC3ANbEjI987tZLv60TWQG///77snv3bunTp09grgMHDpTp06fL8OHDa+6+urpaevToIatXr5bevXvLqFGjZMiQITJx4kQM2K9GrGfTBI71pClvABMMGAN2C2JNzGDAboxVrQsLC6Vnz55i/jezbdmyRWbOnCmbNm0K/rRu3TpZuHBhYMiNbT4GTCMU1Y2n5CB41B8omGDAGLBbAtPEjI987tZLv60TWQFn3+K+ffvk8ssvl/Xr10uvXr1qdq1YsUJKS0ulpKQk+Nv27dtlzJgxsm3btkgNeM/BPXLvT++VH9zyA+nSoYvf0Ujp2TSBk9JbzbnbMMGAMeCcwyVoqIkZDNiNsVPrI0eOyODBg4Ol53vuuafWscaAV65cKUuXLg3+Xl5eLmPHjq1nwIsWLRLzL7NVVFTI8uXLnfqR3fjp956WJTuXyPiu44N/bCKVlZWSn58PiiwCMKktB3jAw5YgNBoxq6Im96d1S2wFbJ7x3nrrrdK9e3d56KGH6vHdunWrzJgxo2YJ2lTICxYsiHwJ2lTAs1fMlgdvfpAK+OSoaGauaQ2YXPsNEypgKuBco+VEO03MUAG7Mc659R133CHHjx+XxYsXS4sWLeodZwzaPBc2z3zNIIwePVoGDRrES1g5E/bXUBM4/q6ezDPBBAPGgN1iUxMzGLAb45xav/jii3LttdfKpZdeGnwMyWy333679O3bV4qKiqSsrCz424YNG2Tq1Kl8DCknqtE10gROdL1JxplhggFjwG6xqIkZDNiNceytfQyYRiix33iEHYBHfbgwwYAxYLeko4kZH/ncrZd+Wyf2GbDf2/zibD4GTCOUqO4nCeeFBwZs0yEaYUIShUZ85HNbv6LcjwEr6JJMSCY22aARNEIFbIuS8BrBgN0Yx97ax4CRXMMHTuxCiLgDaASNYMBuQaaJGR/53K2XfltTASt4aoSiuExqDoEHS9A2saIRJiRRaAQDtlFN2H4fA0YyIZnYZI1G0AgVsC1KwmvERz5366Xf1lTACp4k1/CBo8CeqkPQCBrBgN1CVhMzGLAb49hb+xgwjVBiv/EIOwAPlqBt8kIjTEii0IiPfG7rV5T7qYAVdEkmJBObbNAIGqECtkVJeI1gwG6MY2/tY8BIruEDJ3YhRNwBNIJGMGC3INPEjI987tZLv62pgBU8NUJRXCY1h8CDJWibWNEIE5IoNIIB26gmbL+PASOZkExsskYjaIQK2BYl4TXiI5+79dJvaypgBU+Sa/jAUWBP1SFoBI1gwG4hq4kZDNiNceytfQyYRiix33iEHYAHS9A2eaERJiRRaMRHPrf1K8r9VMAKuiQTkolNNmgEjVAB26IkvEYwYDfGsbf2MWAk1/CBE7sQIu4AGkEjGLBbkGlixkc+d+ul39ZUwAqeGqEoLpOaQ+DBErRNrGiECUkUGsGAbVQTtt/HgJFMSCY2WaMRNEIFbIuS8Brxkc/deum3NRWwgifJNXzgKLCn6hA0gkYwYLeQ1cQMBuzGOPbWPgZMI5TYbzzCDsCDJWibvNAIE5IoNOIjn9v6FeV+KmAFXZIJycQmGzSCRqiAbVESXiMYsBvj2Fv7GDCSa/jAiV0IEXcAjaARDNgtyDQx4yOfu/XSb2sqYAVPjVAUl0nNIfBgCdomVjTChCQKjWDANqoJ2+9jwEgmJBObrNEIGqECtkVJeI34yOduvfTbmgpYwZPkGj5wFNhTdQgaQSMYsFvIamIGA3ZjHHtrHwOmEUrsNx5hB+DBErRNXmiECUkUGvGRz239inI/FbCCLsmEZGKTDRpBI1TAtigJrxEM2I1xTq0LCwultLRU9u7dK0ePHm3wmG7dukl+fr60atUq2L9s2TIxg2HbfAwYyTV84NjGKe370QgawYDdolgTMz7yuVsv/bZOZAW8efNm6dGjh1x44YWNGrBpV1BQ4ETEx4BphOLUyZQ1hgdL0DbJohEmJFFoxEc+t/Uryv2JNODMDefl5WHAUY6+p3OTXDFgm5TQCAYchUYwYBvVEPttBtypUyc5duyYDBs2TObOnSumvW3zMWAkE5KJTWdoBI2wBG2LkvAa8ZHP3Xrpt3VqK+Bdu3YFy88HDx6UcePGSd++fWXWrFn16CxatEjMv8xWUVEhy5cvD0WxsrIyeP7MdoIAPOorASa1mcADHrZ8qdGIeV+ovLzcdurE7k+tAWcTXbNmjSxevDh4ccu2+ZgxUd2En7naxint+9EIGqECdotiTcz4yOduvfTbOpUGbGZK1dXV0rFjx+AZ8aRJk6Rr164yb948Kx0fA6YRirVjKW4Aj/qDBxMMGAN2S2qamPGRz9166bd1Ig148uTJsnbtWtm9e3fwJvTQoUMDky0qKpKysjLZsWOHjBgxInj+a4y4X79+Mn/+fGnbtq2Vjo8B0wjF2rEUN4AHBmyTLxphQhKFRnzkc1u/otyfSAOO8oZ9DBjJhGRi0ygaQSNUwLYoCa8RH/ncrZd+W2PACp4k1/CBo8CeqkPQCBrBgN1CVhMzGLAb49hb+xgwjVBiv/EIOwAPlqBt8kIjTEii0IiPfG7rV5T7qYAVdEkmJBObbNAIGqECtkVJeI1gwG6MY2/tY8BIruEDJ3YhRNwBNIJGMGC3INPEjI987tZLv62pgBU8NUJRXCY1h8CDJWibWNEIE5IoNIIB26gmbL+PASOZkExsskYjaIQK2BYl4TXiI5+79dJvaypgBU+Sa/jAUWBP1SFoBI1gwG4hq4kZDNiNceytfQyYRiix33iEHYAHS9A2eaERJiRRaMRHPrf1K8r9VMAKuiQTkolNNmgEjVAB26IkvEYwYDfGsbf2MWAk1/CBE7sQIu4AGkEjGLBbkGlixkc+d+ul39ZUwAqeGqEoLpOaQ+DBErRNrGiECUkUGsGAbVQTtt/HgJFMSCY2WaMRNEIFbIuS8Brxkc/deum3NRWwgifJNXzgKLCn6hA0gkYwYLeQ1cQMBuzGOPbWPgZMI5TYbzzCDsCDJWibvNAIE5IoNOIjn9v6FeV+KmAFXZIJycQmGzSCRqiAbVESXiMYsBvj2Fv7GDCSa/jAiV0IEXcAjaARDNgtyDQx4yOfu/XSb2sqYAVPjVAUl0nNIfBgCdomVjTChCQKjWDANqoJ2+9jwEgmJBObrNEIGqECtkVJeI34yOduvfTbmgpYwZPkGj5wFNhTdQgaQSMYsFvIamIGA3ZjHHtrHwOmEUrsNx5hB+DBErRNXmiECUkUGvGRz239inI/FbCCLsmEZGKTDRpBI1TAtigJrxEM2I1x7K19DBjJNXzgxC6EiDuARtAIBuwWZJqY8ZHP3XrptzUVsIKnRiiKy6TmEHiwBG0TKxphQhKFRjBgG9WE7fcxYCQTkolN1mgEjVAB26IkvEZ85HO3XvptTQWs4ElyDR84CuypOgSNoBEM2C1kNTGDAbsxjr21jwHTCCX2G4+wA/BgCdomLzTChCQKjfjI57Z+RbmfClhBl2RCMrHJBo2gESpgW5SE1wgG7MY4p9aFhYVSWloqe/fulaNHjzZ4zMaNG2XKlClSVVUl/fv3l+LiYsnLy7Oe38eAkVzDB451oFLeAI2gEQzYLYg1MeMjn7v10m/rRFbAmzdvlh49esiFF17YoAFXV1cH+1evXi29e/eWUaNGyZAhQ2TixIlWOj4GTCMUa8dS3AAeLEHb5ItGmJBEoREf+dzWryj3J9KAMzdsKtqGKuAtW7bIzJkzZdOmTUHTdevWycKFCwNDtm0+BoxkQjKx6QyNoBEqYFuUhNeIj3zu1ku/rVNpwCtWrAiWqEtKSgIa27dvlzFjxsi2bdusdHwMGMk1fOBYByrlDdAIGsGA3YJYEzM+8rlbL/22Tq0Br1y5UpYuXRrQKC8vl7FjxzZowIsWLRLzL7NVVFTI8uXLQ1GsrKyU/Pz8UOdoSgfDo/5owqQ2E3jAw5bzNBox7wuZ/J/WLZUGvHXrVpkxY0bNEvT69etlwYIFLEHHpELNzDWmrp62y8KECpgK2C3cNDFDBezG2Kn1qZ4Bm5ewevbsGRiuGYDRo0fLoEGDeAnLia6/xprA8Xf1ZJ4JJhgwBuwWm5qYwYDdGOfUevLkybJ27VrZvXt38Cb00KFDZdKkSVJUVCRlZWXBOTZs2CBTp07lY0g5EY22kSZwou1R/GeHCQaMAbvFoSZmMGA3xrG39jFgGqHEfuMRdgAe9eHCBAPGgN2SjiZmfORzt176bZ3oZ8B+b/XE2XwMmEYoUdxLUs4JDwzYpkU0woQkCo34yOe2fkW5HwNW0CWZkExsskEjaIQK2BYl4TWCAbsxjr21jwEjuYYPnNiFEHEH0AgawYDdgkwTMz7yuVsv/bamAlbw1AhFcZnUHAIPlqBtYkUjTEii0AgGbKOasP0+BoxkQjKxyRqNoBEqYFuUhNeIj3zu1ku/ramAFTxJruEDR4E9VYegETSCAbuFrCZmMGA3xrG39jFgGqHEfuMRdgAeLEHb5IVGmJBEoREf+dzWryj3UwEr6JJMSCY22aARNEIFbIuS8BrBgN0Yx97ax4CRXMMHTuxCiLgDaASNYMBuQaaJGR/53K2XfltTASt4aoSiuExqDoEHS9A2saIRJiRRaAQDtlFN2H4fA0YyIZnYZI1G0AgVsC1KwmvERz5366Xf1lTACp4k1/CBo8CeqkPQCBrBgN1CVhMzGLAb49hb+xgwjVBiv/EIOwAPlqBt8kIjTEii0IiPfG7rV5T7qYAVdEkmJBObbNAIGqECtkVJeI1gwG6MY2/tY8BIruEDJ3YhRNwBNIJGMGC3INPEjI987tZLv62pgBU8NUJRXCY1h8CDJWibWNEIE5IoNIIB26gmbL+PASOZkExsskYjaIQK2BYl4TXiI5+79dJvaypgBU+Sa/jAUWBP1SFoBI1gwG4hq4kZDNiNceytfQyYRiix33iEHYAHS9A2eaERJiRRaMRHPrf1K8r9VMAKuiQTkolNNmgEjVAB26IkvEYwYDfGsbf2MWAk1/CBE7sQIu4AGkEjGLBbkGlixkc+d+ul39ZUwAqeGqEoLpOaQ+DBErRNrGiECUkUGsGAbVQTtt/HgJFMSCY2WaMRNEIFbIuS8Brxkc/deum3NRWwgifJNXzgKLCn6hA0gkYwYLeQ1cQMBuzGOPbWPgZMI5TYbzzCDsCDJWibvNAIE5IoNOIjn9v6FeV+KmAFXZIJycQmGzSCRqiAbVESXiMYsBvjnFtv3LhRpkyZIlVVVdK/f38pLi6WvLy8Wsd369ZN8vPzpVWrVsHfly1bJmZAGtt8DBjJNXzg5CyElDZEI2gEA3YLXk3M+Mjnbr302zqRFXB1dbX06NFDVq9eLb1795ZRo0bJkCFDZOLEifUMePPmzVJQUJAzFR8DphFKzh1MYUN4sARtky0aYUIShUZ85HNbv6Lcn0gD3rJli8ycOVM2bdoU3Pu6detk4cKFgSFnb6YCxoCjlEdu5ya5YsA2paARDDgKjWDANqqK/StWrJDS0lIpKSkJjt6+fbuMGTNGtm3bVs+AO3XqJMeOHZNhw4bJ3Llz6y1T1728jwEjmZBMbLJGI2ikMY2gDz+TVh/53BbLUe5PZAVsDHjlypWydOnS4N7Ly8tl7Nix9Qx4165dwfLzwYMHZdy4cdK3b1+ZNWtWLV6LFi0S8y+zVVRUyPLly0MxraysDJ49s50gAI/6SoBJbSbwgIctX2o0UlhYGPhDWrdEGvDWrVtlxowZNUvQ69evlwULFtRbgs6GvmbNGlm8eHFQOTe2+ZgxMXulurEFPBpBI1TAtigJrxEf+dytl35bJ9KAzUtYPXv2DAzXAB49erQMGjSo1ktYZrZk2nXs2FGOHj0qkyZNkq5du8q8efMwYL8asZ4Ns6mPCCbhk6tVeClugD78xAwGHFEQbNiwQaZOnVrrY0ivvvqqFBUVSVlZmezYsUNGjBgRPP81RtyvXz+ZP3++tG3bFgOOaExOdVqSiZ9kcpqH7bReDo0wIbEJTqMRDNhGNWH7fQyYRigJw+C1O/DAgG2CQiMYcBQa8ZHPbf2Kcn8il6CjvGEfA0YyIZnYNIpG0EhjGkEffiatPvK5LZaj3I8BK+gSPCRXm2zQCBrBgG1REl4jGLAb49hb+xgwkmv4wIldCBF3AI2gEQzYLcg0MeMjn7v10m9rKmAFT41QFJdJzSHw8LOclpoBV3QUjTAhsclGoxEM2EY1Yft9DJhGKAnD4LU78MCAbYJCIxhwFBrxkc9t/YpyPxWwgi7JhGRikw0aQSMsQduiJLxGMGA3xrG39jFgJNfwgRO7ECLuABpBIxiwW5BpYsZHPnfrpd/WVMAKnhqhKC6TmkPgwRK0TaxohAlJFBrBgG1UE7bfx4CRTEgmNlmjETRCBWyLkvAa8ZHP3XrptzUVsIInyTV84Ciwp+oQNIJGMGC3kNXEDAbsxjj21j4GTCOU2G88wg7AgyVom7zQCBOSKDTiI5/b+hXlfipgBV2SCcnEJhs0gkaogG1REl4jGLAb49hb+xgwkmv4wIldCBF3AI2gEQzYLcg0MeMjn7v10m9rKmAFT41QFJdJzSHwYAnaJlY0woQkCo1gwDaqCdvvY8BIJiQTm6zRCBqhArZFSXiN+Mjnbr3025oKWMGT5Bo+cBTYU3UIGkEjGLBbyGpiBgN2Yxx7ax8DphFK7DceYQfgwRK0TV5ohAlJFBrxkc9t/YpyPxWwgi7JhGRikw0aQSNUwLYoCa8RDNiNceytfQwYyTV84MQuhIg7gEbQCAbsFmSamPGRz9166bc1FbCCp0Yoisuk5hB4sARtEysaYUIShUYwYBvVhO33MWAkE5KJTdZoBI1QAduiJLxGfORzt176bU0FrOBJcg0fOArsqToEjaARDNgtZDUxgwG7MY69tY8B0wgl9huPsAPwYAnaJi80woQkCo34yOe2fkW5nwpYQZdkQjKxyQaNoBEqYFuUhNcIBuzGOPbWPgaM5Bo+cGIXQsQdQCNoBAN2CzJNzPjI52699NuaCljBUyMUxWVScwg8WIK2iRWNMCGJQiMYsI1qwvb7GDCSCcnEJms0gkaogG1REl4jPvK5Wy/9tk5sBbxx40aZMmWKVFVVSf/+/aW4uFjy8vJq3X0uberi8jFgJNfwgeNXxsk7GxpBIxiwW1xqYsZHPnfrpd/WiTTg6upq6dGjh6xevVp69+4to0aNkiFDhsjEiRNr7j6XNg2h8jFgGqH4HbZknQ0eLEHbFIlGmJBEoREf+dzWryj3J9KAt2zZIjNnzpRNmzYF975u3TpZuHBhYMiZLZc2GHCU0vni3CRXDNimNDSCAUehEQzYRlWxf8WKFVJaWiolJSXB0du3b5cxY8bItm3bas6WS5soDHjPwT1y70/vlR/c8gPp0qGL4u6a3iEkVwzYpmo0ggFHoREM2EZVsd+Y68qVK2Xp0qXB0eXl5TJ27Nh6BmxrY45dtGhR8C+zVVRUyPLlyxW9OnHI0+89LUt2LpHxXccH/9hEKisrJT8/HxRZBGBSWw7wgIctQWg0UlhYGPhDWrdELkFv3bpVZsyYUbMEvX79elmwYEGtJehc2kRVAc9eMVsevPlBKuCTgKluqIBtCRCNUAFHoREqYBtVxX7zglXPnj0DwzWAR48eLYMGDar3EpatTRQGbM5JMiGZ2GSNRtBIYxpBH34mrRiwLRMp92/YsEGmTp1a62NIr776qhQVFUlZWVlw1oba1P2oUt3L+xgwgofkapM1GkEjGLAtSsJrxEc+d+ul39aJXIL2e4u1z+ZjwEiu4QMnyjFOwrnRCBrBgN0iURMzPvK5Wy/9tsaAFTw1QlFcJjWHwMPPclpqBlzRUTTChMQmG41GMGAb1YTt9zFgGqEkDIPX7sADA7YJCo1gwFFoxEc+t/Uryv1UwAq6JBOSiU02aASNsARti5LwGsGA3RjH3trHgJFcwwdO7EKIuANoBI1gwG5BpokZH/ncrZd+W1MBK3hqhKK4TGoOgQdL0DaxohEmJFFoBAO2UU3Yfh8DRjIhmdhkjUbQCBWwLUrCa8RHPnfrpd/WVMAKniTX8IGjwJ6qQ9AIGsGA3UJWEzMYsBvj2Ft37NhRCgoKQvXj448/lk6dOoU6R1M6GB71RxMmtZnAAx62nKfRyK5du+TAgQO2Uyd2f7OrgH2MRNpnXT4YZJ8DHvWJwqQ2E3jAw5Z3mqNGMGCbKhrY3xyF0hgmeGDAtjBCIxgwGqlPAAO2qQIDthIiuWLANpGgEQwYjWDANg3ktN/8vvCUKVNyatscGsGj/ijDpDYTeMDDlgubo0aogG2qYD8EIAABCEAgAgIYcARQOSUEIAABCEDARgADthFiPwQgAAEIQCACAhiwA9SNGzcGz36rqqqkf//+UlxcLHl5eQ5nSF/TnTt3yoQJE2TPnj3SsmVLuemmm+T+++8PbmTmzJny85//XM444wx54IEH5Oabbw7+bo4ZM2aMVFRUSOfOneUnP/mJdOnSJX03b+nx3XffHWjg6NGjzZ7Hp59+KobHli1bAj3cc889Mnny5GarkV/+8pdy7733Brpo166dLF68WHr16tWseBQWFkppaans3bu3Jka0eeOZZ56RoqIiqa6ulltvvTXIN01hw4BzHEUz8D169JDVq1dL7969ZdSoUTJkyBCZOHFijmdIZ7P3339fdu/eLX369AkmHgMHDpTp06fLmWeeGRjxhg0bAqO9+uqrpby8XDp06BCY73XXXSd33nmn/Od//qds3bpVnn766XQCOEWvf/3rX8uTTz4pJSUlQXJZv359s+Zhxvriiy8ODOb48ePy4YcfyquvvtpsmXTt2lXWrVsXmK6ZpD3//PMyadKkZsVj8+bNQc688MILawxYEyeffPKJXHbZZfLb3/5WvvzlLwfFz7//+7/L3/zN36Q+p2DAOQ6hmdmb5LJp06bgCBNcCxcuDAy5OW1mVtuzZ0/53//9X7nqqqvk9ttvD27/tttuCyrgESNGBN8SZma9xqQrKyuDbx4z33LTVLYjR47I9ddfLytXrgwqfGPA3/ve95otj4MHD8oll1wif/rTn2qtCDVnJl/96ldl+fLl8td//dfy0EMPBatCZgLbHGPGrBJmVok0mjDVb1lZmfz3f/93kEIef/xxefPNN2XBggWpTykYcI5DuGLFimA5xVQ8Ztu+fXtQ6W3bti3HM6S/2b59++Tyyy8Pqr0ZM2bIP/7jPwYVsdlmzZoVLDOPHTtWvvGNbwRVc2Y7//zz5Y9//KOcddZZ6YcgIv/8z/8sF110UTD5yCSXG2+8sdnyeO2114LHFMZsTJXyla98RebPny9Tp05ttkzMRN1MRtu2bSv5+fny4osvyne+851mySPbgDVx8sQTTwQTeFP1mu25554LVhVMPk77hgHnOILGgE3Fs3Tp0uAIs9xqzKa5GLCp+gYPHizDhw8Pnu+ZQPqnf/on+da3vhXwMKsDZqnJMDEmbb6jNbOdd9558vbbbzcJA3799ddl2rRpwZJiixYtahlwc+Rhxvj3v/+9XHnllUGVYh7LmKX5ZcuWBc8+myMT87jKxMcPf/jDYOn0qaeekp/97GeBXpojj7oG7MrAGLBZhs68e2J0Zv6GAedoXk2hmXmOaaq+zBK0qQLNEkhzWILOvPjQvXv3YDnNbHfddVeQdDNL0GY1YOTIkfWWoA8dOhQYc1NZgn700Ufl+9//vrRu3Trg8N5774lZbjTG0xx5GAbmHQDzTVdmhcRsZszNaoh5LNEcmZgJiVkdMlWv2czSs3ksM378+GbJI9uANXnj2WeflbVr19YsQZvq94033mAJuikYa673YEzIPPs0hmuSzejRo2XQoEFN/iUsw+eOO+4IXqwxb3KaWbzZTAVY9yUs81zYvIRlqmDzEpZ56cQYlnl+3tRewsroJpNcmjuPAQMGyMMPPxy8rPeLX/wiqP7mzp3bLDViXlw0la9ZmjeTz1WrVsm//du/yYMPPtgseWQbsCZO9u/fX/MS1osGAOYAAAIMSURBVLnnnhvkFjMJ5iWsXN2ribQzb/ya51rN6WNIZhZ/7bXXyqWXXhp8DMlspur9h3/4h5qPVBhTNh8LuOWWW4L92R9DuuCCC4KPIZlE1BS37OSS+VhWc+RhHsmYiZp56e7ss88OXpTJ/thNc2PyX//1X/KjH/0oeETRvn374NMA5t2I5qQR8zE0U7ma90FM/A8dOjTQhYaBeRHrX//1X+XYsWPBJ1DMZKYpbDwDbgqjyD1AAAIQgEDqCGDAqRsyOgwBCEAAAk2BAAbcFEaRe4AABCAAgdQRwIBTN2R0GAIQgAAEmgIBDLgpjCL3AAEIQAACqSOAAaduyOgwBCAAAQg0BQIYcFMYRe4BAhCAAARSRwADTt2Q0WEIQAACEGgKBDDgpjCK3AMEIAABCKSOAAacuiGjwxCAAAQg0BQIYMBNYRS5BwhAAAIQSB0BDDh1Q0aHIQABCECgKRDAgJvCKHIPEIAABCCQOgIYcOqGjA5DAAIQgEBTIIABN4VR5B4gAAEIQCB1BDDg1A0ZHYYABCAAgaZAAANuCqPIPUAAAhCAQOoIYMCpGzI6DAEIQAACTYEABtwURpF7gAAEIACB1BHAgFM3ZHQYAhCAAASaAgEMuCmMIvcAAQhAAAKpI4ABp27I6DAEIAABCDQFAhhwUxhF7gECEIAABFJHAANO3ZDRYQhAAAIQaAoE/j+Lzz+KQx85mAAAAABJRU5ErkJggg==\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Last estimate is: 3.195195195195195\n"
     ]
    }
   ],
   "source": [
    "NUMBER_OF_SAMPLES = 10**3\n",
    "TIMES_TO_REDRAW_PLOT = 100\n",
    "\n",
    "_REDRAW_EVERY_X = NUMBER_OF_SAMPLES/TIMES_TO_REDRAW_PLOT\n",
    "\n",
    "pi_estimate = []  # list of estimate at each sample point\n",
    "\n",
    "f = IntProgress(min=1, max=NUMBER_OF_SAMPLES)\n",
    "display(f)\n",
    "print(f\"Simulating {NUMBER_OF_SAMPLES} tries...\")\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "def plot_estimate():\n",
    "    ax.clear()\n",
    "    ax.grid(True)\n",
    "    ax.plot(pi_estimate, marker='o', markersize=1, color='g',linestyle = 'None')\n",
    "    ax.axhline(y=3.1415, xmin=0, xmax=3, c=\"black\", linewidth=2, zorder=0)\n",
    "    \n",
    "    fig.canvas.draw()\n",
    "\n",
    "inside_cnt, outside_cnt = 0, 0  # global count of points\n",
    "_estimate = 0\n",
    "\n",
    "for i in range(1, NUMBER_OF_SAMPLES):\n",
    "    f.value += 1\n",
    "#     for j in range(i):\n",
    "    x = -1 + 2*random.random()\n",
    "    y = -1 + 2*random.random()\n",
    "    if math.sqrt(x**2 + y**2) < 1:\n",
    "        inside_cnt += 1\n",
    "    else:\n",
    "        outside_cnt+= 1\n",
    "    _estimate = 4*inside_cnt/(inside_cnt+outside_cnt)\n",
    "    pi_estimate += _estimate,  # NOTE: apparently adding tuples to a list is faster\n",
    "    if not (i % _REDRAW_EVERY_X): plot_estimate()\n",
    "\n",
    "print(f\"Last estimate is: {_estimate}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "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",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}