stats_challenge2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import bokeh.layouts as bkl\n",
    "import bokeh.plotting as bk\n",
    "import bokeh.transform as btr\n",
    "from bokeh.models import *\n",
    "from bokeh.palettes import *\n",
    "from bokeh.io import output_notebook, show\n",
    "from bokeh.plotting import figure"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let the current fraction of the population which is sick be $x_0$.  To simplify things, suppose that everybody has the same transmission probability.  You’ll often see this talked about as $R_0$, or the number of people who every sick person will infect by the time they recover.  Thus, the fraction of the infected population next week will be $R_0 * x$, and after $n$ iterations, $x_n = {R_0}^n * x_0$.  If $R_0 < 1$, then eventually the virus must die out.  If $R_0 > 1$, it increases exponentially. \n",
    "\n",
    "That’s actually only a valid approximation for small x; let’s see if we can make a slightly better approximation which can work even when much of the population is sick at the same time.  Instead, we’re going to assume that you can only transmit the virus to people who are not currently sick.  Thus,\n",
    " \n",
    "$x_{k+1} = R_0 * x_k * (1 – x_k)$.\n",
    " \n",
    "Mathematically, this is valid for $0 \\leq R_0 \\leq 4$, since the maximum possible value of $x(1-x)$ is $¼$ (at $x = ½$). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot(Rmin,Rmax,n_range=25):\n",
    "    n = [n for n in range(0, n_range)]\n",
    "    x = np.zeros(len(n))\n",
    "\n",
    "    source = ColumnDataSource(data=dict(n=n, x=x))\n",
    "\n",
    "    plot = figure(width=400, height=400, x_range=(0, n_range), y_range=(0, 1))\n",
    "\n",
    "    plot.line('n', 'x', source=source, line_width=3, line_alpha=0.6)\n",
    "\n",
    "    Rslider = Slider(start=Rmin, end=Rmax, value=Rmin, step=.001, title=\"R_0\")\n",
    "    x0slider = Slider(start=0, end=1, value=0, step=.001, title=\"x_0\")\n",
    "\n",
    "    callback = CustomJS(args=dict(source=source, Rslider=Rslider,x0slider=x0slider), code=\"\"\"\n",
    "        const R = Rslider.value\n",
    "        const x0 = x0slider.value\n",
    "        const n = source.data.n\n",
    "        let x = Array(n.length).fill(0)\n",
    "        x[0] = x0\n",
    "        for (var i = 1; i < n.length+1; i++) {\n",
    "            x[i] = R*x[i-1]*(1-x[i-1])\n",
    "        }\n",
    "\n",
    "        source.data = { n, x }\n",
    "    \"\"\")\n",
    "\n",
    "    Rslider.js_on_change('value', callback)\n",
    "    x0slider.js_on_change('value', callback)\n",
    "\n",
    "    layout = bkl.column(Rslider, x0slider, plot)\n",
    "\n",
    "    output_notebook()\n",
    "    show(layout)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$R_0 < 1$.  Write some code in your favorite programming language to take an initial, random value of $x_0$ and then plot $x_n$ and see what happens over time.  What is the long-term behavior if $R_0 < 1$?  Does it match what you expected from before?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       "        .bk-notebook-logo {\n",
       "            display: block;\n",
       "            width: 20px;\n",
       "            height: 20px;\n",
       "            background-image: url(data:image/png;base64,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);\n",
       "        }\n",
       "    </style>\n",
       "    <div>\n",
       "        <a href=\"https://bokeh.org\" target=\"_blank\" class=\"bk-notebook-logo\"></a>\n",
       "        <span id=\"da8de1f2-f4dd-46d4-be0c-f7f1a1d37004\">Loading BokehJS ...</span>\n",
       "    </div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": "(function(root) {\n  function now() {\n    return new Date();\n  }\n\n  const force = true;\n\n  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n    root._bokeh_onload_callbacks = [];\n    root._bokeh_is_loading = undefined;\n  }\n\nconst JS_MIME_TYPE = 'application/javascript';\n  const HTML_MIME_TYPE = 'text/html';\n  const EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n  const CLASS_NAME = 'output_bokeh rendered_html';\n\n  /**\n   * Render data to the DOM node\n   */\n  function render(props, node) {\n    const script = document.createElement(\"script\");\n    node.appendChild(script);\n  }\n\n  /**\n   * Handle when an output is cleared or removed\n   */\n  function handleClearOutput(event, handle) {\n    const cell = handle.cell;\n\n    const id = cell.output_area._bokeh_element_id;\n    const server_id = cell.output_area._bokeh_server_id;\n    // Clean up Bokeh references\n    if (id != null && id in Bokeh.index) {\n      Bokeh.index[id].model.document.clear();\n      delete Bokeh.index[id];\n    }\n\n    if (server_id !== undefined) {\n      // Clean up Bokeh references\n      const cmd_clean = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n      cell.notebook.kernel.execute(cmd_clean, {\n        iopub: {\n          output: function(msg) {\n            const id = msg.content.text.trim();\n            if (id in Bokeh.index) {\n              Bokeh.index[id].model.document.clear();\n              delete Bokeh.index[id];\n            }\n          }\n        }\n      });\n      // Destroy server and session\n      const cmd_destroy = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n      cell.notebook.kernel.execute(cmd_destroy);\n    }\n  }\n\n  /**\n   * Handle when a new output is added\n   */\n  function handleAddOutput(event, handle) {\n    const output_area = handle.output_area;\n    const output = handle.output;\n\n    // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n    if ((output.output_type != \"display_data\") || (!Object.prototype.hasOwnProperty.call(output.data, EXEC_MIME_TYPE))) {\n      return\n    }\n\n    const toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n\n    if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n      toinsert[toinsert.length - 1].firstChild.textContent = output.data[JS_MIME_TYPE];\n      // store reference to embed id on output_area\n      output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n    }\n    if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n      const bk_div = document.createElement(\"div\");\n      bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n      const script_attrs = bk_div.children[0].attributes;\n      for (let i = 0; i < script_attrs.length; i++) {\n        toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n        toinsert[toinsert.length - 1].firstChild.textContent = bk_div.children[0].textContent\n      }\n      // store reference to server id on output_area\n      output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n    }\n  }\n\n  function register_renderer(events, OutputArea) {\n\n    function append_mime(data, metadata, element) {\n      // create a DOM node to render to\n      const toinsert = this.create_output_subarea(\n        metadata,\n        CLASS_NAME,\n        EXEC_MIME_TYPE\n      );\n      this.keyboard_manager.register_events(toinsert);\n      // Render to node\n      const props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n      render(props, toinsert[toinsert.length - 1]);\n      element.append(toinsert);\n      return toinsert\n    }\n\n    /* Handle when an output is cleared or removed */\n    events.on('clear_output.CodeCell', handleClearOutput);\n    events.on('delete.Cell', handleClearOutput);\n\n    /* Handle when a new output is added */\n    events.on('output_added.OutputArea', handleAddOutput);\n\n    /**\n     * Register the mime type and append_mime function with output_area\n     */\n    OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n      /* Is output safe? */\n      safe: true,\n      /* Index of renderer in `output_area.display_order` */\n      index: 0\n    });\n  }\n\n  // register the mime type if in Jupyter Notebook environment and previously unregistered\n  if (root.Jupyter !== undefined) {\n    const events = require('base/js/events');\n    const OutputArea = require('notebook/js/outputarea').OutputArea;\n\n    if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n      register_renderer(events, OutputArea);\n    }\n  }\n  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n    root._bokeh_timeout = Date.now() + 5000;\n    root._bokeh_failed_load = false;\n  }\n\n  const NB_LOAD_WARNING = {'data': {'text/html':\n     \"<div style='background-color: #fdd'>\\n\"+\n     \"<p>\\n\"+\n     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    const el = document.getElementById(\"da8de1f2-f4dd-46d4-be0c-f7f1a1d37004\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) {\n        if (callback != null)\n          callback();\n      });\n    } finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.debug(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(css_urls, js_urls, callback) {\n    if (css_urls == null) css_urls = [];\n    if (js_urls == null) js_urls = [];\n\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n    function on_load() {\n      root._bokeh_is_loading--;\n      if (root._bokeh_is_loading === 0) {\n        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n        run_callbacks()\n      }\n    }\n\n    function on_error(url) {\n      console.error(\"failed to load \" + url);\n    }\n\n    for (let i = 0; i < css_urls.length; i++) {\n      const url = css_urls[i];\n      const element = document.createElement(\"link\");\n      element.onload = on_load;\n      element.onerror = on_error.bind(null, url);\n      element.rel = \"stylesheet\";\n      element.type = \"text/css\";\n      element.href = url;\n      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n      document.body.appendChild(element);\n    }\n\n    for (let i = 0; i < js_urls.length; i++) {\n      const url = js_urls[i];\n      const element = document.createElement('script');\n      element.onload = on_load;\n      element.onerror = on_error.bind(null, url);\n      element.async = false;\n      element.src = url;\n      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.head.appendChild(element);\n    }\n  };\n\n  function inject_raw_css(css) {\n    const element = document.createElement(\"style\");\n    element.appendChild(document.createTextNode(css));\n    document.body.appendChild(element);\n  }\n\n  const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-3.1.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-3.1.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-3.1.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-3.1.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-3.1.1.min.js\"];\n  const css_urls = [];\n\n  const inline_js = [    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\nfunction(Bokeh) {\n    }\n  ];\n\n  function run_inline_js() {\n    if (root.Bokeh !== undefined || force === true) {\n          for (let i = 0; i < inline_js.length; i++) {\n      inline_js[i].call(root, root.Bokeh);\n    }\nif (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      const cell = $(document.getElementById(\"da8de1f2-f4dd-46d4-be0c-f7f1a1d37004\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(css_urls, js_urls, function() {\n      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));",
      "application/vnd.bokehjs_load.v0+json": ""
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "  <div id=\"f2b4982a-4051-4369-83dc-81d85d2cbfff\" data-root-id=\"p1940\" style=\"display: contents;\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": "(function(root) {\n  function embed_document(root) {\n  const docs_json = {\"bf7be3c0-2dc3-4e1f-be23-6ccc5d6298f2\":{\"version\":\"3.1.1\",\"title\":\"Bokeh Application\",\"defs\":[],\"roots\":[{\"type\":\"object\",\"name\":\"Column\",\"id\":\"p1940\",\"attributes\":{\"children\":[{\"type\":\"object\",\"name\":\"Slider\",\"id\":\"p1937\",\"attributes\":{\"js_property_callbacks\":{\"type\":\"map\",\"entries\":[[\"change:value\",[{\"type\":\"object\",\"name\":\"CustomJS\",\"id\":\"p1939\",\"attributes\":{\"args\":{\"type\":\"map\",\"entries\":[[\"source\",{\"type\":\"object\",\"name\":\"ColumnDataSource\",\"id\":\"p1879\",\"attributes\":{\"selected\":{\"type\":\"object\",\"name\":\"Selection\",\"id\":\"p1881\",\"attributes\":{\"indices\":[],\"line_indices\":[]}},\"selection_policy\":{\"type\":\"object\",\"name\":\"UnionRenderers\",\"id\":\"p1880\"},\"data\":{\"type\":\"map\",\"entries\":[[\"n\",[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24]],[\"x\",{\"type\":\"ndarray\",\"array\":{\"type\":\"bytes\",\"data\":\"AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA=\"},\"shape\":[25],\"dtype\":\"float64\",\"order\":\"little\"}]]}}}],[\"Rslider\",{\"id\":\"p1937\"}],[\"x0slider\",{\"type\":\"object\",\"name\":\"Slider\",\"id\":\"p1938\",\"attributes\":{\"js_property_callbacks\":{\"type\":\"map\",\"entries\":[[\"change:value\",[{\"id\":\"p1939\"}]]]},\"title\":\"x_0\",\"start\":0,\"end\":1,\"value\":0,\"step\":0.001}}]]},\"code\":\"\\n        const R = Rslider.value\\n        const x0 = x0slider.value\\n        const n = source.data.n\\n        let x = Array(n.length).fill(0)\\n        x[0] = x0\\n        for (var i = 1; i < n.length+1; i++) {\\n            x[i] = R*x[i-1]*(1-x[i-1])\\n        }\\n\\n        source.data = { n, x }\\n    \"}}]]]},\"title\":\"R_0\",\"start\":0,\"end\":1,\"value\":0,\"step\":0.001}},{\"id\":\"p1938\"},{\"type\":\"object\",\"name\":\"Figure\",\"id\":\"p1882\",\"attributes\":{\"width\":400,\"height\":400,\"x_range\":{\"type\":\"object\",\"name\":\"Range1d\",\"id\":\"p1891\",\"attributes\":{\"end\":25}},\"y_range\":{\"type\":\"object\",\"name\":\"Range1d\",\"id\":\"p1893\"},\"x_scale\":{\"type\":\"object\",\"name\":\"LinearScale\",\"id\":\"p1895\"},\"y_scale\":{\"type\":\"object\",\"name\":\"LinearScale\",\"id\":\"p1897\"},\"title\":{\"type\":\"object\",\"name\":\"Title\",\"id\":\"p1888\"},\"renderers\":[{\"type\":\"object\",\"name\":\"GlyphRenderer\",\"id\":\"p1934\",\"attributes\":{\"data_source\":{\"id\":\"p1879\"},\"view\":{\"type\":\"object\",\"name\":\"CDSView\",\"id\":\"p1935\",\"attributes\":{\"filter\":{\"type\":\"object\",\"name\":\"AllIndices\",\"id\":\"p1936\"}}},\"glyph\":{\"type\":\"object\",\"name\":\"Line\",\"id\":\"p1931\",\"attributes\":{\"x\":{\"type\":\"field\",\"field\":\"n\"},\"y\":{\"type\":\"field\",\"field\":\"x\"},\"line_color\":\"#1f77b4\",\"line_alpha\":0.6,\"line_width\":3}},\"nonselection_glyph\":{\"type\":\"object\",\"name\":\"Line\",\"id\":\"p1932\",\"attributes\":{\"x\":{\"type\":\"field\",\"field\":\"n\"},\"y\":{\"type\":\"field\",\"field\":\"x\"},\"line_color\":\"#1f77b4\",\"line_alpha\":0.1,\"line_width\":3}},\"muted_glyph\":{\"type\":\"object\",\"name\":\"Line\",\"id\":\"p1933\",\"attributes\":{\"x\":{\"type\":\"field\",\"field\":\"n\"},\"y\":{\"type\":\"field\",\"field\":\"x\"},\"line_color\":\"#1f77b4\",\"line_alpha\":0.2,\"line_width\":3}}}}],\"toolbar\":{\"type\":\"object\",\"name\":\"Toolbar\",\"id\":\"p1890\",\"attributes\":{\"tools\":[{\"type\":\"object\",\"name\":\"PanTool\",\"id\":\"p1913\"},{\"type\":\"object\",\"name\":\"WheelZoomTool\",\"id\":\"p1914\"},{\"type\":\"object\",\"name\":\"BoxZoomTool\",\"id\":\"p1915\",\"attributes\":{\"overlay\":{\"type\":\"object\",\"name\":\"BoxAnnotation\",\"id\":\"p1916\",\"attributes\":{\"syncable\":false,\"level\":\"overlay\",\"visible\":false,\"left_units\":\"canvas\",\"right_units\":\"canvas\",\"bottom_units\":\"canvas\",\"top_units\":\"canvas\",\"line_color\":\"black\",\"line_alpha\":1.0,\"line_width\":2,\"line_dash\":[4,4],\"fill_color\":\"lightgrey\",\"fill_alpha\":0.5}}}},{\"type\":\"object\",\"name\":\"SaveTool\",\"id\":\"p1917\"},{\"type\":\"object\",\"name\":\"ResetTool\",\"id\":\"p1918\"},{\"type\":\"object\",\"name\":\"HelpTool\",\"id\":\"p1919\"}]}},\"left\":[{\"type\":\"object\",\"name\":\"LinearAxis\",\"id\":\"p1906\",\"attributes\":{\"ticker\":{\"type\":\"object\",\"name\":\"BasicTicker\",\"id\":\"p1907\",\"attributes\":{\"mantissas\":[1,2,5]}},\"formatter\":{\"type\":\"object\",\"name\":\"BasicTickFormatter\",\"id\":\"p1908\"},\"major_label_policy\":{\"type\":\"object\",\"name\":\"AllLabels\",\"id\":\"p1909\"}}}],\"below\":[{\"type\":\"object\",\"name\":\"LinearAxis\",\"id\":\"p1899\",\"attributes\":{\"ticker\":{\"type\":\"object\",\"name\":\"BasicTicker\",\"id\":\"p1900\",\"attributes\":{\"mantissas\":[1,2,5]}},\"formatter\":{\"type\":\"object\",\"name\":\"BasicTickFormatter\",\"id\":\"p1901\"},\"major_label_policy\":{\"type\":\"object\",\"name\":\"AllLabels\",\"id\":\"p1902\"}}}],\"center\":[{\"type\":\"object\",\"name\":\"Grid\",\"id\":\"p1905\",\"attributes\":{\"axis\":{\"id\":\"p1899\"}}},{\"type\":\"object\",\"name\":\"Grid\",\"id\":\"p1912\",\"attributes\":{\"dimension\":1,\"axis\":{\"id\":\"p1906\"}}}]}}]}}],\"callbacks\":{\"type\":\"map\"}}};\n  const render_items = [{\"docid\":\"bf7be3c0-2dc3-4e1f-be23-6ccc5d6298f2\",\"roots\":{\"p1940\":\"f2b4982a-4051-4369-83dc-81d85d2cbfff\"},\"root_ids\":[\"p1940\"]}];\n  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n  }\n  if (root.Bokeh !== undefined) {\n    embed_document(root);\n  } else {\n    let attempts = 0;\n    const timer = setInterval(function(root) {\n      if (root.Bokeh !== undefined) {\n        clearInterval(timer);\n        embed_document(root);\n      } else {\n        attempts++;\n        if (attempts > 100) {\n          clearInterval(timer);\n          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n        }\n      }\n    }, 10, root)\n  }\n})(window);",
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "p1940"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(0,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$R_0 = 2$ and $R_0 = 2.5$.  Use the same code, but now try some values of $R_0 > 1$.  Now what happens? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       "        .bk-notebook-logo {\n",
       "            display: block;\n",
       "            width: 20px;\n",
       "            height: 20px;\n",
       "            background-image: url(data:image/png;base64,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);\n",
       "        }\n",
       "    </style>\n",
       "    <div>\n",
       "        <a href=\"https://bokeh.org\" target=\"_blank\" class=\"bk-notebook-logo\"></a>\n",
       "        <span id=\"da758993-211d-4c01-865d-ae1a70475721\">Loading BokehJS ...</span>\n",
       "    </div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": "(function(root) {\n  function now() {\n    return new Date();\n  }\n\n  const force = true;\n\n  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n    root._bokeh_onload_callbacks = [];\n    root._bokeh_is_loading = undefined;\n  }\n\nconst JS_MIME_TYPE = 'application/javascript';\n  const HTML_MIME_TYPE = 'text/html';\n  const EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n  const CLASS_NAME = 'output_bokeh rendered_html';\n\n  /**\n   * Render data to the DOM node\n   */\n  function render(props, node) {\n    const script = document.createElement(\"script\");\n    node.appendChild(script);\n  }\n\n  /**\n   * Handle when an output is cleared or removed\n   */\n  function handleClearOutput(event, handle) {\n    const cell = handle.cell;\n\n    const id = cell.output_area._bokeh_element_id;\n    const server_id = cell.output_area._bokeh_server_id;\n    // Clean up Bokeh references\n    if (id != null && id in Bokeh.index) {\n      Bokeh.index[id].model.document.clear();\n      delete Bokeh.index[id];\n    }\n\n    if (server_id !== undefined) {\n      // Clean up Bokeh references\n      const cmd_clean = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n      cell.notebook.kernel.execute(cmd_clean, {\n        iopub: {\n          output: function(msg) {\n            const id = msg.content.text.trim();\n            if (id in Bokeh.index) {\n              Bokeh.index[id].model.document.clear();\n              delete Bokeh.index[id];\n            }\n          }\n        }\n      });\n      // Destroy server and session\n      const cmd_destroy = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n      cell.notebook.kernel.execute(cmd_destroy);\n    }\n  }\n\n  /**\n   * Handle when a new output is added\n   */\n  function handleAddOutput(event, handle) {\n    const output_area = handle.output_area;\n    const output = handle.output;\n\n    // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n    if ((output.output_type != \"display_data\") || (!Object.prototype.hasOwnProperty.call(output.data, EXEC_MIME_TYPE))) {\n      return\n    }\n\n    const toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n\n    if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n      toinsert[toinsert.length - 1].firstChild.textContent = output.data[JS_MIME_TYPE];\n      // store reference to embed id on output_area\n      output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n    }\n    if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n      const bk_div = document.createElement(\"div\");\n      bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n      const script_attrs = bk_div.children[0].attributes;\n      for (let i = 0; i < script_attrs.length; i++) {\n        toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n        toinsert[toinsert.length - 1].firstChild.textContent = bk_div.children[0].textContent\n      }\n      // store reference to server id on output_area\n      output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n    }\n  }\n\n  function register_renderer(events, OutputArea) {\n\n    function append_mime(data, metadata, element) {\n      // create a DOM node to render to\n      const toinsert = this.create_output_subarea(\n        metadata,\n        CLASS_NAME,\n        EXEC_MIME_TYPE\n      );\n      this.keyboard_manager.register_events(toinsert);\n      // Render to node\n      const props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n      render(props, toinsert[toinsert.length - 1]);\n      element.append(toinsert);\n      return toinsert\n    }\n\n    /* Handle when an output is cleared or removed */\n    events.on('clear_output.CodeCell', handleClearOutput);\n    events.on('delete.Cell', handleClearOutput);\n\n    /* Handle when a new output is added */\n    events.on('output_added.OutputArea', handleAddOutput);\n\n    /**\n     * Register the mime type and append_mime function with output_area\n     */\n    OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n      /* Is output safe? */\n      safe: true,\n      /* Index of renderer in `output_area.display_order` */\n      index: 0\n    });\n  }\n\n  // register the mime type if in Jupyter Notebook environment and previously unregistered\n  if (root.Jupyter !== undefined) {\n    const events = require('base/js/events');\n    const OutputArea = require('notebook/js/outputarea').OutputArea;\n\n    if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n      register_renderer(events, OutputArea);\n    }\n  }\n  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n    root._bokeh_timeout = Date.now() + 5000;\n    root._bokeh_failed_load = false;\n  }\n\n  const NB_LOAD_WARNING = {'data': {'text/html':\n     \"<div style='background-color: #fdd'>\\n\"+\n     \"<p>\\n\"+\n     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    const el = document.getElementById(\"da758993-211d-4c01-865d-ae1a70475721\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) {\n        if (callback != null)\n          callback();\n      });\n    } finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.debug(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(css_urls, js_urls, callback) {\n    if (css_urls == null) css_urls = [];\n    if (js_urls == null) js_urls = [];\n\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n    function on_load() {\n      root._bokeh_is_loading--;\n      if (root._bokeh_is_loading === 0) {\n        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n        run_callbacks()\n      }\n    }\n\n    function on_error(url) {\n      console.error(\"failed to load \" + url);\n    }\n\n    for (let i = 0; i < css_urls.length; i++) {\n      const url = css_urls[i];\n      const element = document.createElement(\"link\");\n      element.onload = on_load;\n      element.onerror = on_error.bind(null, url);\n      element.rel = \"stylesheet\";\n      element.type = \"text/css\";\n      element.href = url;\n      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n      document.body.appendChild(element);\n    }\n\n    for (let i = 0; i < js_urls.length; i++) {\n      const url = js_urls[i];\n      const element = document.createElement('script');\n      element.onload = on_load;\n      element.onerror = on_error.bind(null, url);\n      element.async = false;\n      element.src = url;\n      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.head.appendChild(element);\n    }\n  };\n\n  function inject_raw_css(css) {\n    const element = document.createElement(\"style\");\n    element.appendChild(document.createTextNode(css));\n    document.body.appendChild(element);\n  }\n\n  const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-3.1.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-3.1.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-3.1.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-3.1.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-3.1.1.min.js\"];\n  const css_urls = [];\n\n  const inline_js = [    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\nfunction(Bokeh) {\n    }\n  ];\n\n  function run_inline_js() {\n    if (root.Bokeh !== undefined || force === true) {\n          for (let i = 0; i < inline_js.length; i++) {\n      inline_js[i].call(root, root.Bokeh);\n    }\nif (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      const cell = $(document.getElementById(\"da758993-211d-4c01-865d-ae1a70475721\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(css_urls, js_urls, function() {\n      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));",
      "application/vnd.bokehjs_load.v0+json": ""
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "  <div id=\"f07a348c-895f-41e9-aad3-078c45e06529\" data-root-id=\"p2160\" style=\"display: contents;\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": "(function(root) {\n  function embed_document(root) {\n  const docs_json = {\"7e55a334-9b9c-47b6-97fd-9ded005384e1\":{\"version\":\"3.1.1\",\"title\":\"Bokeh Application\",\"defs\":[],\"roots\":[{\"type\":\"object\",\"name\":\"Column\",\"id\":\"p2160\",\"attributes\":{\"children\":[{\"type\":\"object\",\"name\":\"Slider\",\"id\":\"p2157\",\"attributes\":{\"js_property_callbacks\":{\"type\":\"map\",\"entries\":[[\"change:value\",[{\"type\":\"object\",\"name\":\"CustomJS\",\"id\":\"p2159\",\"attributes\":{\"args\":{\"type\":\"map\",\"entries\":[[\"source\",{\"type\":\"object\",\"name\":\"ColumnDataSource\",\"id\":\"p2099\",\"attributes\":{\"selected\":{\"type\":\"object\",\"name\":\"Selection\",\"id\":\"p2101\",\"attributes\":{\"indices\":[],\"line_indices\":[]}},\"selection_policy\":{\"type\":\"object\",\"name\":\"UnionRenderers\",\"id\":\"p2100\"},\"data\":{\"type\":\"map\",\"entries\":[[\"n\",[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24]],[\"x\",{\"type\":\"ndarray\",\"array\":{\"type\":\"bytes\",\"data\":\"AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA=\"},\"shape\":[25],\"dtype\":\"float64\",\"order\":\"little\"}]]}}}],[\"Rslider\",{\"id\":\"p2157\"}],[\"x0slider\",{\"type\":\"object\",\"name\":\"Slider\",\"id\":\"p2158\",\"attributes\":{\"js_property_callbacks\":{\"type\":\"map\",\"entries\":[[\"change:value\",[{\"id\":\"p2159\"}]]]},\"title\":\"x_0\",\"start\":0,\"end\":1,\"value\":0,\"step\":0.001}}]]},\"code\":\"\\n        const R = Rslider.value\\n        const x0 = x0slider.value\\n        const n = source.data.n\\n        let x = Array(n.length).fill(0)\\n        x[0] = x0\\n        for (var i = 1; i < n.length+1; i++) {\\n            x[i] = R*x[i-1]*(1-x[i-1])\\n        }\\n\\n        source.data = { n, x }\\n    \"}}]]]},\"title\":\"R_0\",\"start\":1,\"end\":2.5,\"value\":1,\"step\":0.001}},{\"id\":\"p2158\"},{\"type\":\"object\",\"name\":\"Figure\",\"id\":\"p2102\",\"attributes\":{\"width\":400,\"height\":400,\"x_range\":{\"type\":\"object\",\"name\":\"Range1d\",\"id\":\"p2111\",\"attributes\":{\"end\":25}},\"y_range\":{\"type\":\"object\",\"name\":\"Range1d\",\"id\":\"p2113\"},\"x_scale\":{\"type\":\"object\",\"name\":\"LinearScale\",\"id\":\"p2115\"},\"y_scale\":{\"type\":\"object\",\"name\":\"LinearScale\",\"id\":\"p2117\"},\"title\":{\"type\":\"object\",\"name\":\"Title\",\"id\":\"p2108\"},\"renderers\":[{\"type\":\"object\",\"name\":\"GlyphRenderer\",\"id\":\"p2154\",\"attributes\":{\"data_source\":{\"id\":\"p2099\"},\"view\":{\"type\":\"object\",\"name\":\"CDSView\",\"id\":\"p2155\",\"attributes\":{\"filter\":{\"type\":\"object\",\"name\":\"AllIndices\",\"id\":\"p2156\"}}},\"glyph\":{\"type\":\"object\",\"name\":\"Line\",\"id\":\"p2151\",\"attributes\":{\"x\":{\"type\":\"field\",\"field\":\"n\"},\"y\":{\"type\":\"field\",\"field\":\"x\"},\"line_color\":\"#1f77b4\",\"line_alpha\":0.6,\"line_width\":3}},\"nonselection_glyph\":{\"type\":\"object\",\"name\":\"Line\",\"id\":\"p2152\",\"attributes\":{\"x\":{\"type\":\"field\",\"field\":\"n\"},\"y\":{\"type\":\"field\",\"field\":\"x\"},\"line_color\":\"#1f77b4\",\"line_alpha\":0.1,\"line_width\":3}},\"muted_glyph\":{\"type\":\"object\",\"name\":\"Line\",\"id\":\"p2153\",\"attributes\":{\"x\":{\"type\":\"field\",\"field\":\"n\"},\"y\":{\"type\":\"field\",\"field\":\"x\"},\"line_color\":\"#1f77b4\",\"line_alpha\":0.2,\"line_width\":3}}}}],\"toolbar\":{\"type\":\"object\",\"name\":\"Toolbar\",\"id\":\"p2110\",\"attributes\":{\"tools\":[{\"type\":\"object\",\"name\":\"PanTool\",\"id\":\"p2133\"},{\"type\":\"object\",\"name\":\"WheelZoomTool\",\"id\":\"p2134\"},{\"type\":\"object\",\"name\":\"BoxZoomTool\",\"id\":\"p2135\",\"attributes\":{\"overlay\":{\"type\":\"object\",\"name\":\"BoxAnnotation\",\"id\":\"p2136\",\"attributes\":{\"syncable\":false,\"level\":\"overlay\",\"visible\":false,\"left_units\":\"canvas\",\"right_units\":\"canvas\",\"bottom_units\":\"canvas\",\"top_units\":\"canvas\",\"line_color\":\"black\",\"line_alpha\":1.0,\"line_width\":2,\"line_dash\":[4,4],\"fill_color\":\"lightgrey\",\"fill_alpha\":0.5}}}},{\"type\":\"object\",\"name\":\"SaveTool\",\"id\":\"p2137\"},{\"type\":\"object\",\"name\":\"ResetTool\",\"id\":\"p2138\"},{\"type\":\"object\",\"name\":\"HelpTool\",\"id\":\"p2139\"}]}},\"left\":[{\"type\":\"object\",\"name\":\"LinearAxis\",\"id\":\"p2126\",\"attributes\":{\"ticker\":{\"type\":\"object\",\"name\":\"BasicTicker\",\"id\":\"p2127\",\"attributes\":{\"mantissas\":[1,2,5]}},\"formatter\":{\"type\":\"object\",\"name\":\"BasicTickFormatter\",\"id\":\"p2128\"},\"major_label_policy\":{\"type\":\"object\",\"name\":\"AllLabels\",\"id\":\"p2129\"}}}],\"below\":[{\"type\":\"object\",\"name\":\"LinearAxis\",\"id\":\"p2119\",\"attributes\":{\"ticker\":{\"type\":\"object\",\"name\":\"BasicTicker\",\"id\":\"p2120\",\"attributes\":{\"mantissas\":[1,2,5]}},\"formatter\":{\"type\":\"object\",\"name\":\"BasicTickFormatter\",\"id\":\"p2121\"},\"major_label_policy\":{\"type\":\"object\",\"name\":\"AllLabels\",\"id\":\"p2122\"}}}],\"center\":[{\"type\":\"object\",\"name\":\"Grid\",\"id\":\"p2125\",\"attributes\":{\"axis\":{\"id\":\"p2119\"}}},{\"type\":\"object\",\"name\":\"Grid\",\"id\":\"p2132\",\"attributes\":{\"dimension\":1,\"axis\":{\"id\":\"p2126\"}}}]}}]}}],\"callbacks\":{\"type\":\"map\"}}};\n  const render_items = [{\"docid\":\"7e55a334-9b9c-47b6-97fd-9ded005384e1\",\"roots\":{\"p2160\":\"f07a348c-895f-41e9-aad3-078c45e06529\"},\"root_ids\":[\"p2160\"]}];\n  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n  }\n  if (root.Bokeh !== undefined) {\n    embed_document(root);\n  } else {\n    let attempts = 0;\n    const timer = setInterval(function(root) {\n      if (root.Bokeh !== undefined) {\n        clearInterval(timer);\n        embed_document(root);\n      } else {\n        attempts++;\n        if (attempts > 100) {\n          clearInterval(timer);\n          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n        }\n      }\n    }, 10, root)\n  }\n})(window);",
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "p2160"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(1,2.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Show that this behavior should only work for $1 < R_0 < 3$.  If you’ve got a bit of calculus, you’ll have some good tools to prove your answer, but otherwise, try values of $R_0$ in that range and see if you can figure out what’s going on.\n",
    "\n",
    "It turns out this new behavior also doesn’t work all the way up to $R_0 = 4$.  Look at a few other values; you’ll find that $R_0 = 3.5, 3.55,$ and $3.833$ are interesting choices.\n",
    "\n",
    "Finally, look at $R_0 = 4$.  Can you explain what’s happening here?  The answer to this is probably not going to be intuitive if you haven’t run into it before, but that’s going to be what we discuss on Friday, followed by building a mini-numerical “simulation” to explore it for next week.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       "        .bk-notebook-logo {\n",
       "            display: block;\n",
       "            width: 20px;\n",
       "            height: 20px;\n",
       "            background-image: url(data:image/png;base64,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);\n",
       "        }\n",
       "    </style>\n",
       "    <div>\n",
       "        <a href=\"https://bokeh.org\" target=\"_blank\" class=\"bk-notebook-logo\"></a>\n",
       "        <span id=\"a016cacb-36de-415a-9f18-f28673cd54d8\">Loading BokehJS ...</span>\n",
       "    </div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": "(function(root) {\n  function now() {\n    return new Date();\n  }\n\n  const force = true;\n\n  if (typeof root._bokeh_onload_callbacks === \"undefined\" || force === true) {\n    root._bokeh_onload_callbacks = [];\n    root._bokeh_is_loading = undefined;\n  }\n\nconst JS_MIME_TYPE = 'application/javascript';\n  const HTML_MIME_TYPE = 'text/html';\n  const EXEC_MIME_TYPE = 'application/vnd.bokehjs_exec.v0+json';\n  const CLASS_NAME = 'output_bokeh rendered_html';\n\n  /**\n   * Render data to the DOM node\n   */\n  function render(props, node) {\n    const script = document.createElement(\"script\");\n    node.appendChild(script);\n  }\n\n  /**\n   * Handle when an output is cleared or removed\n   */\n  function handleClearOutput(event, handle) {\n    const cell = handle.cell;\n\n    const id = cell.output_area._bokeh_element_id;\n    const server_id = cell.output_area._bokeh_server_id;\n    // Clean up Bokeh references\n    if (id != null && id in Bokeh.index) {\n      Bokeh.index[id].model.document.clear();\n      delete Bokeh.index[id];\n    }\n\n    if (server_id !== undefined) {\n      // Clean up Bokeh references\n      const cmd_clean = \"from bokeh.io.state import curstate; print(curstate().uuid_to_server['\" + server_id + \"'].get_sessions()[0].document.roots[0]._id)\";\n      cell.notebook.kernel.execute(cmd_clean, {\n        iopub: {\n          output: function(msg) {\n            const id = msg.content.text.trim();\n            if (id in Bokeh.index) {\n              Bokeh.index[id].model.document.clear();\n              delete Bokeh.index[id];\n            }\n          }\n        }\n      });\n      // Destroy server and session\n      const cmd_destroy = \"import bokeh.io.notebook as ion; ion.destroy_server('\" + server_id + \"')\";\n      cell.notebook.kernel.execute(cmd_destroy);\n    }\n  }\n\n  /**\n   * Handle when a new output is added\n   */\n  function handleAddOutput(event, handle) {\n    const output_area = handle.output_area;\n    const output = handle.output;\n\n    // limit handleAddOutput to display_data with EXEC_MIME_TYPE content only\n    if ((output.output_type != \"display_data\") || (!Object.prototype.hasOwnProperty.call(output.data, EXEC_MIME_TYPE))) {\n      return\n    }\n\n    const toinsert = output_area.element.find(\".\" + CLASS_NAME.split(' ')[0]);\n\n    if (output.metadata[EXEC_MIME_TYPE][\"id\"] !== undefined) {\n      toinsert[toinsert.length - 1].firstChild.textContent = output.data[JS_MIME_TYPE];\n      // store reference to embed id on output_area\n      output_area._bokeh_element_id = output.metadata[EXEC_MIME_TYPE][\"id\"];\n    }\n    if (output.metadata[EXEC_MIME_TYPE][\"server_id\"] !== undefined) {\n      const bk_div = document.createElement(\"div\");\n      bk_div.innerHTML = output.data[HTML_MIME_TYPE];\n      const script_attrs = bk_div.children[0].attributes;\n      for (let i = 0; i < script_attrs.length; i++) {\n        toinsert[toinsert.length - 1].firstChild.setAttribute(script_attrs[i].name, script_attrs[i].value);\n        toinsert[toinsert.length - 1].firstChild.textContent = bk_div.children[0].textContent\n      }\n      // store reference to server id on output_area\n      output_area._bokeh_server_id = output.metadata[EXEC_MIME_TYPE][\"server_id\"];\n    }\n  }\n\n  function register_renderer(events, OutputArea) {\n\n    function append_mime(data, metadata, element) {\n      // create a DOM node to render to\n      const toinsert = this.create_output_subarea(\n        metadata,\n        CLASS_NAME,\n        EXEC_MIME_TYPE\n      );\n      this.keyboard_manager.register_events(toinsert);\n      // Render to node\n      const props = {data: data, metadata: metadata[EXEC_MIME_TYPE]};\n      render(props, toinsert[toinsert.length - 1]);\n      element.append(toinsert);\n      return toinsert\n    }\n\n    /* Handle when an output is cleared or removed */\n    events.on('clear_output.CodeCell', handleClearOutput);\n    events.on('delete.Cell', handleClearOutput);\n\n    /* Handle when a new output is added */\n    events.on('output_added.OutputArea', handleAddOutput);\n\n    /**\n     * Register the mime type and append_mime function with output_area\n     */\n    OutputArea.prototype.register_mime_type(EXEC_MIME_TYPE, append_mime, {\n      /* Is output safe? */\n      safe: true,\n      /* Index of renderer in `output_area.display_order` */\n      index: 0\n    });\n  }\n\n  // register the mime type if in Jupyter Notebook environment and previously unregistered\n  if (root.Jupyter !== undefined) {\n    const events = require('base/js/events');\n    const OutputArea = require('notebook/js/outputarea').OutputArea;\n\n    if (OutputArea.prototype.mime_types().indexOf(EXEC_MIME_TYPE) == -1) {\n      register_renderer(events, OutputArea);\n    }\n  }\n  if (typeof (root._bokeh_timeout) === \"undefined\" || force === true) {\n    root._bokeh_timeout = Date.now() + 5000;\n    root._bokeh_failed_load = false;\n  }\n\n  const NB_LOAD_WARNING = {'data': {'text/html':\n     \"<div style='background-color: #fdd'>\\n\"+\n     \"<p>\\n\"+\n     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n     \"</p>\\n\"+\n     \"<ul>\\n\"+\n     \"<li>re-rerun `output_notebook()` to attempt to load from CDN again, or</li>\\n\"+\n     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n     \"</ul>\\n\"+\n     \"<code>\\n\"+\n     \"from bokeh.resources import INLINE\\n\"+\n     \"output_notebook(resources=INLINE)\\n\"+\n     \"</code>\\n\"+\n     \"</div>\"}};\n\n  function display_loaded() {\n    const el = document.getElementById(\"a016cacb-36de-415a-9f18-f28673cd54d8\");\n    if (el != null) {\n      el.textContent = \"BokehJS is loading...\";\n    }\n    if (root.Bokeh !== undefined) {\n      if (el != null) {\n        el.textContent = \"BokehJS \" + root.Bokeh.version + \" successfully loaded.\";\n      }\n    } else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(display_loaded, 100)\n    }\n  }\n\n  function run_callbacks() {\n    try {\n      root._bokeh_onload_callbacks.forEach(function(callback) {\n        if (callback != null)\n          callback();\n      });\n    } finally {\n      delete root._bokeh_onload_callbacks\n    }\n    console.debug(\"Bokeh: all callbacks have finished\");\n  }\n\n  function load_libs(css_urls, js_urls, callback) {\n    if (css_urls == null) css_urls = [];\n    if (js_urls == null) js_urls = [];\n\n    root._bokeh_onload_callbacks.push(callback);\n    if (root._bokeh_is_loading > 0) {\n      console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n      return null;\n    }\n    if (js_urls == null || js_urls.length === 0) {\n      run_callbacks();\n      return null;\n    }\n    console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n    root._bokeh_is_loading = css_urls.length + js_urls.length;\n\n    function on_load() {\n      root._bokeh_is_loading--;\n      if (root._bokeh_is_loading === 0) {\n        console.debug(\"Bokeh: all BokehJS libraries/stylesheets loaded\");\n        run_callbacks()\n      }\n    }\n\n    function on_error(url) {\n      console.error(\"failed to load \" + url);\n    }\n\n    for (let i = 0; i < css_urls.length; i++) {\n      const url = css_urls[i];\n      const element = document.createElement(\"link\");\n      element.onload = on_load;\n      element.onerror = on_error.bind(null, url);\n      element.rel = \"stylesheet\";\n      element.type = \"text/css\";\n      element.href = url;\n      console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n      document.body.appendChild(element);\n    }\n\n    for (let i = 0; i < js_urls.length; i++) {\n      const url = js_urls[i];\n      const element = document.createElement('script');\n      element.onload = on_load;\n      element.onerror = on_error.bind(null, url);\n      element.async = false;\n      element.src = url;\n      console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n      document.head.appendChild(element);\n    }\n  };\n\n  function inject_raw_css(css) {\n    const element = document.createElement(\"style\");\n    element.appendChild(document.createTextNode(css));\n    document.body.appendChild(element);\n  }\n\n  const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-3.1.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-3.1.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-3.1.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-3.1.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-3.1.1.min.js\"];\n  const css_urls = [];\n\n  const inline_js = [    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\nfunction(Bokeh) {\n    }\n  ];\n\n  function run_inline_js() {\n    if (root.Bokeh !== undefined || force === true) {\n          for (let i = 0; i < inline_js.length; i++) {\n      inline_js[i].call(root, root.Bokeh);\n    }\nif (force === true) {\n        display_loaded();\n      }} else if (Date.now() < root._bokeh_timeout) {\n      setTimeout(run_inline_js, 100);\n    } else if (!root._bokeh_failed_load) {\n      console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n      root._bokeh_failed_load = true;\n    } else if (force !== true) {\n      const cell = $(document.getElementById(\"a016cacb-36de-415a-9f18-f28673cd54d8\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\n  }\n\n  if (root._bokeh_is_loading === 0) {\n    console.debug(\"Bokeh: BokehJS loaded, going straight to plotting\");\n    run_inline_js();\n  } else {\n    load_libs(css_urls, js_urls, function() {\n      console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n      run_inline_js();\n    });\n  }\n}(window));",
      "application/vnd.bokehjs_load.v0+json": ""
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "\n",
       "  <div id=\"fe3628a3-7fca-4073-8d11-f503e321c9c7\" data-root-id=\"p2394\" style=\"display: contents;\"></div>\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": "(function(root) {\n  function embed_document(root) {\n  const docs_json = {\"3511810d-0be9-4e38-90dd-10dbd33c599f\":{\"version\":\"3.1.1\",\"title\":\"Bokeh Application\",\"defs\":[],\"roots\":[{\"type\":\"object\",\"name\":\"Column\",\"id\":\"p2394\",\"attributes\":{\"children\":[{\"type\":\"object\",\"name\":\"Slider\",\"id\":\"p2391\",\"attributes\":{\"js_property_callbacks\":{\"type\":\"map\",\"entries\":[[\"change:value\",[{\"type\":\"object\",\"name\":\"CustomJS\",\"id\":\"p2393\",\"attributes\":{\"args\":{\"type\":\"map\",\"entries\":[[\"source\",{\"type\":\"object\",\"name\":\"ColumnDataSource\",\"id\":\"p2333\",\"attributes\":{\"selected\":{\"type\":\"object\",\"name\":\"Selection\",\"id\":\"p2335\",\"attributes\":{\"indices\":[],\"line_indices\":[]}},\"selection_policy\":{\"type\":\"object\",\"name\":\"UnionRenderers\",\"id\":\"p2334\"},\"data\":{\"type\":\"map\",\"entries\":[[\"n\",[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249]],[\"x\",{\"type\":\"ndarray\",\"array\":{\"type\":\"bytes\",\"data\":\"AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA=\"},\"shape\":[250],\"dtype\":\"float64\",\"order\":\"little\"}]]}}}],[\"Rslider\",{\"id\":\"p2391\"}],[\"x0slider\",{\"type\":\"object\",\"name\":\"Slider\",\"id\":\"p2392\",\"attributes\":{\"js_property_callbacks\":{\"type\":\"map\",\"entries\":[[\"change:value\",[{\"id\":\"p2393\"}]]]},\"title\":\"x_0\",\"start\":0,\"end\":1,\"value\":0,\"step\":0.001}}]]},\"code\":\"\\n        const R = Rslider.value\\n        const x0 = x0slider.value\\n        const n = source.data.n\\n        let x = Array(n.length).fill(0)\\n        x[0] = x0\\n        for (var i = 1; i < n.length+1; i++) {\\n            x[i] = R*x[i-1]*(1-x[i-1])\\n        }\\n\\n        source.data = { n, x }\\n    \"}}]]]},\"title\":\"R_0\",\"start\":0.9,\"end\":4,\"value\":0.9,\"step\":0.001}},{\"id\":\"p2392\"},{\"type\":\"object\",\"name\":\"Figure\",\"id\":\"p2336\",\"attributes\":{\"width\":400,\"height\":400,\"x_range\":{\"type\":\"object\",\"name\":\"Range1d\",\"id\":\"p2345\",\"attributes\":{\"end\":250}},\"y_range\":{\"type\":\"object\",\"name\":\"Range1d\",\"id\":\"p2347\"},\"x_scale\":{\"type\":\"object\",\"name\":\"LinearScale\",\"id\":\"p2349\"},\"y_scale\":{\"type\":\"object\",\"name\":\"LinearScale\",\"id\":\"p2351\"},\"title\":{\"type\":\"object\",\"name\":\"Title\",\"id\":\"p2342\"},\"renderers\":[{\"type\":\"object\",\"name\":\"GlyphRenderer\",\"id\":\"p2388\",\"attributes\":{\"data_source\":{\"id\":\"p2333\"},\"view\":{\"type\":\"object\",\"name\":\"CDSView\",\"id\":\"p2389\",\"attributes\":{\"filter\":{\"type\":\"object\",\"name\":\"AllIndices\",\"id\":\"p2390\"}}},\"glyph\":{\"type\":\"object\",\"name\":\"Line\",\"id\":\"p2385\",\"attributes\":{\"x\":{\"type\":\"field\",\"field\":\"n\"},\"y\":{\"type\":\"field\",\"field\":\"x\"},\"line_color\":\"#1f77b4\",\"line_alpha\":0.6,\"line_width\":3}},\"nonselection_glyph\":{\"type\":\"object\",\"name\":\"Line\",\"id\":\"p2386\",\"attributes\":{\"x\":{\"type\":\"field\",\"field\":\"n\"},\"y\":{\"type\":\"field\",\"field\":\"x\"},\"line_color\":\"#1f77b4\",\"line_alpha\":0.1,\"line_width\":3}},\"muted_glyph\":{\"type\":\"object\",\"name\":\"Line\",\"id\":\"p2387\",\"attributes\":{\"x\":{\"type\":\"field\",\"field\":\"n\"},\"y\":{\"type\":\"field\",\"field\":\"x\"},\"line_color\":\"#1f77b4\",\"line_alpha\":0.2,\"line_width\":3}}}}],\"toolbar\":{\"type\":\"object\",\"name\":\"Toolbar\",\"id\":\"p2344\",\"attributes\":{\"tools\":[{\"type\":\"object\",\"name\":\"PanTool\",\"id\":\"p2367\"},{\"type\":\"object\",\"name\":\"WheelZoomTool\",\"id\":\"p2368\"},{\"type\":\"object\",\"name\":\"BoxZoomTool\",\"id\":\"p2369\",\"attributes\":{\"overlay\":{\"type\":\"object\",\"name\":\"BoxAnnotation\",\"id\":\"p2370\",\"attributes\":{\"syncable\":false,\"level\":\"overlay\",\"visible\":false,\"left_units\":\"canvas\",\"right_units\":\"canvas\",\"bottom_units\":\"canvas\",\"top_units\":\"canvas\",\"line_color\":\"black\",\"line_alpha\":1.0,\"line_width\":2,\"line_dash\":[4,4],\"fill_color\":\"lightgrey\",\"fill_alpha\":0.5}}}},{\"type\":\"object\",\"name\":\"SaveTool\",\"id\":\"p2371\"},{\"type\":\"object\",\"name\":\"ResetTool\",\"id\":\"p2372\"},{\"type\":\"object\",\"name\":\"HelpTool\",\"id\":\"p2373\"}]}},\"left\":[{\"type\":\"object\",\"name\":\"LinearAxis\",\"id\":\"p2360\",\"attributes\":{\"ticker\":{\"type\":\"object\",\"name\":\"BasicTicker\",\"id\":\"p2361\",\"attributes\":{\"mantissas\":[1,2,5]}},\"formatter\":{\"type\":\"object\",\"name\":\"BasicTickFormatter\",\"id\":\"p2362\"},\"major_label_policy\":{\"type\":\"object\",\"name\":\"AllLabels\",\"id\":\"p2363\"}}}],\"below\":[{\"type\":\"object\",\"name\":\"LinearAxis\",\"id\":\"p2353\",\"attributes\":{\"ticker\":{\"type\":\"object\",\"name\":\"BasicTicker\",\"id\":\"p2354\",\"attributes\":{\"mantissas\":[1,2,5]}},\"formatter\":{\"type\":\"object\",\"name\":\"BasicTickFormatter\",\"id\":\"p2355\"},\"major_label_policy\":{\"type\":\"object\",\"name\":\"AllLabels\",\"id\":\"p2356\"}}}],\"center\":[{\"type\":\"object\",\"name\":\"Grid\",\"id\":\"p2359\",\"attributes\":{\"axis\":{\"id\":\"p2353\"}}},{\"type\":\"object\",\"name\":\"Grid\",\"id\":\"p2366\",\"attributes\":{\"dimension\":1,\"axis\":{\"id\":\"p2360\"}}}]}}]}}],\"callbacks\":{\"type\":\"map\"}}};\n  const render_items = [{\"docid\":\"3511810d-0be9-4e38-90dd-10dbd33c599f\",\"roots\":{\"p2394\":\"fe3628a3-7fca-4073-8d11-f503e321c9c7\"},\"root_ids\":[\"p2394\"]}];\n  root.Bokeh.embed.embed_items_notebook(docs_json, render_items);\n  }\n  if (root.Bokeh !== undefined) {\n    embed_document(root);\n  } else {\n    let attempts = 0;\n    const timer = setInterval(function(root) {\n      if (root.Bokeh !== undefined) {\n        clearInterval(timer);\n        embed_document(root);\n      } else {\n        attempts++;\n        if (attempts > 100) {\n          clearInterval(timer);\n          console.log(\"Bokeh: ERROR: Unable to run BokehJS code because BokehJS library is missing\");\n        }\n      }\n    }, 10, root)\n  }\n})(window);",
      "application/vnd.bokehjs_exec.v0+json": ""
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "id": "p2394"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(.9,4,n_range=250)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Just for fun, suppose you were running the country at around this time in 2020 and there was an election coming up in 3-4 months.  You’d really like the case count to be low for the election, as it helps your chances of winning.  If I told you that masks reduce $R_0$ from 1.5 to 0.5, are they a good idea?  What about 2.5 to 1.5?  What about 3.5 to 2.5?  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 999999/999999 [00:00<00:00, 3058275.75it/s]\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import tqdm\n",
    "\n",
    "def x_n(n, R=4):\n",
    "    x = 0.4  # Initial value\n",
    "    result = [x]\n",
    "\n",
    "    for _ in tqdm.tqdm(range(1, n)):\n",
    "        x = R * x * (1 - x)\n",
    "        result.append(x)\n",
    "\n",
    "    return result\n",
    "\n",
    "# Generate the values\n",
    "ns = np.arange(0, 1000000)\n",
    "xs = x_n(1000000)\n",
    "\n",
    "plt.plot(ns, xs, linewidth=0.5)\n",
    "plt.xlabel('n')\n",
    "plt.ylabel('x_n')\n",
    "plt.title('Logistic Map')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.225331444259213e-13"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.min(xs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$x_n=4\\,x_{n-1}\\,(1-x_{n-1})$\n",
    "\n",
    "let $x_n=\\sin^2(\\theta_n)\\\\$\n",
    "$\\implies \\theta_n=\\sin^{-1}(\\sqrt{x_n})$\n",
    "and $\\boxed{\\theta_{n+1}}=\\sin^{-1}(\\sqrt{x_{n+1}})=\\sin^{-1}(\\sqrt{4\\,x_n\\,(1-x_n)})=\\sin^{-1}(2\\,\\sqrt{x_n}\\,\\sqrt{1-x_n})=\\sin^{-1}(2\\,\\sin(\\theta_n)\\,\\cos(\\theta_n))=\\sin^{-1}(\\sin(2\\,\\theta_n))=\\boxed{2\\,\\theta_n}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import mpmath\n",
    "\n",
    "# Set the desired precision (number of decimal places)\n",
    "mpmath.mp.dps = 200  # Change this value to the desired precision\n",
    "\n",
    "thetas = [mpmath.power(2, i) for i in range(1, 500)]\n",
    "thetas_mod = [theta % (2 * mpmath.pi) for theta in thetas]\n",
    "xs = [mpmath.power(mpmath.sin(theta), 2) for theta in thetas]\n",
    "xs_mod = [mpmath.power(mpmath.sin(theta), 2) for theta in thetas_mod]\n",
    "\n",
    "# Convert mpmath values to regular Python floats for plotting\n",
    "xs = [float(x) for x in xs]\n",
    "xs_mod = [float(x) for x in xs_mod]\n",
    "\n",
    "plt.plot(xs, label='Original')\n",
    "plt.plot(xs_mod, label='Modified')\n",
    "plt.legend()\n",
    "plt.xlabel('Data Point Index')\n",
    "plt.ylabel('Value of xs')\n",
    "plt.title('Higher Accuracy')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "umap",
   "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": "3.9.16"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}