{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "e68f7f84-3887-4464-99e2-9c759a4d778d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "\n",
    "dim = 2\n",
    "N = 10\n",
    "T_MAX = 101"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "66e49112-405a-4e42-8346-37209a3eeff9",
   "metadata": {},
   "outputs": [],
   "source": [
    "def setup():\n",
    "    x = 2 * (np.random.rand(N,dim) - 0.5)\n",
    "    v = np.zeros((N,dim))\n",
    "    return x, v\n",
    "\n",
    "def leader(t):\n",
    "    return np.array([np.sin(t*0.1), np.cos(t*0.1)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "13963669-d1ce-4d3d-8aa3-17e17fe3df9e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def random(x, leader, k=0.01, k_leader=0.5, **_):\n",
    "    force = np.zeros_like(x)\n",
    "    # add the leader to the list of particles\n",
    "    x = np.vstack([x, leader])\n",
    "    for i in range(N):\n",
    "        for j in range(len(x)):\n",
    "            if j < N:\n",
    "                force[i] += k * (0.7 - np.random.rand(2)) * (x[j] - x[i])\n",
    "            else:\n",
    "                force[i] += k_leader * (0.7 - np.random.rand(2)) * (x[j] - x[i])\n",
    "    return force[:N]\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c73b5de4-dbe6-4cd3-b5f8-97c2f04bfe03",
   "metadata": {},
   "outputs": [],
   "source": [
    "def update(x, v, leader, w=0.5, force=random, **kwargs):\n",
    "    \"\"\" perform the velocity update x(t+1) = x(t) + v(t+1)\n",
    "    input: x(t), v(t)\n",
    "    return: x(t+1), v(t+1)\n",
    "    \"\"\"\n",
    "    v_new = w * v + force(x, leader, **kwargs)\n",
    "    x_new = x + v_new\n",
    "    return x_new, v_new\n",
    "\n",
    "def to_dataframe(x:np.array, v:np.array, t):\n",
    "    \"\"\"converts the particle state at one timestep to a dataframe\"\"\"\n",
    "    df = pd.DataFrame(np.hstack((x, v)), columns=[\"x1\", \"x2\", \"v1\", \"v2\"])\n",
    "    df['t'] = t\n",
    "    df['type'] = \"Follower\"\n",
    "    df = df.append({'x1': leader(t)[0], 'x2': leader(t)[1], 'type': 'Leader', 't': t}, ignore_index=True)\n",
    "    return df\n",
    "\n",
    "def run(force=random, **kwargs):\n",
    "    \"\"\"run an experiment for T_MAX time-steps\"\"\"\n",
    "    data = []\n",
    "    x, v = setup()\n",
    "    for t in range(T_MAX):\n",
    "        x, v = update(x, v, leader(t), force=force, **kwargs)\n",
    "        data.append(to_dataframe(x, v, t))\n",
    "    return pd.concat(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "00df4831-389b-4c29-be4f-40bc00107bd1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "    <div class=\"bk-root\">\n",
       "        <a href=\"https://bokeh.org\" target=\"_blank\" class=\"bk-logo bk-logo-small bk-logo-notebook\"></a>\n",
       "        <span id=\"1002\">Loading BokehJS ...</span>\n",
       "    </div>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/javascript": [
       "\n",
       "(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",
       "\n",
       "  const 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",
       "\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(\"1002\");\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",
       "\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",
       "  \n",
       "  const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-2.4.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-2.4.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.4.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.4.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-2.4.1.min.js\"];\n",
       "  const css_urls = [];\n",
       "  \n",
       "\n",
       "  const inline_js = [\n",
       "    function(Bokeh) {\n",
       "      Bokeh.set_log_level(\"info\");\n",
       "    },\n",
       "    function(Bokeh) {\n",
       "    \n",
       "    \n",
       "    }\n",
       "  ];\n",
       "\n",
       "  function run_inline_js() {\n",
       "    \n",
       "    if (root.Bokeh !== undefined || force === true) {\n",
       "      \n",
       "    for (let i = 0; i < inline_js.length; i++) {\n",
       "      inline_js[i].call(root, root.Bokeh);\n",
       "    }\n",
       "    if (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(\"1002\")).parents('.cell').data().cell;\n",
       "      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
       "    }\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": "\n(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\n  \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(\"1002\");\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\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  \n  const js_urls = [\"https://cdn.bokeh.org/bokeh/release/bokeh-2.4.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-gl-2.4.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-widgets-2.4.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-tables-2.4.1.min.js\", \"https://cdn.bokeh.org/bokeh/release/bokeh-mathjax-2.4.1.min.js\"];\n  const css_urls = [];\n  \n\n  const inline_js = [\n    function(Bokeh) {\n      Bokeh.set_log_level(\"info\");\n    },\n    function(Bokeh) {\n    \n    \n    }\n  ];\n\n  function run_inline_js() {\n    \n    if (root.Bokeh !== undefined || force === true) {\n      \n    for (let i = 0; i < inline_js.length; i++) {\n      inline_js[i].call(root, root.Bokeh);\n    }\n    if (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(\"1002\")).parents('.cell').data().cell;\n      cell.output_area.append_execute_result(NB_LOAD_WARNING)\n    }\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));"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import yaml\n",
    "from bokeh.themes import Theme\n",
    "from bokeh.io import show, output_notebook, curdoc\n",
    "from bokeh.plotting import figure\n",
    "from bokeh.transform import linear_cmap, factor_cmap\n",
    "from bokeh.palettes import Spectral6\n",
    "from bokeh.models import ColumnDataSource, Slider, Column, Toggle\n",
    "from bokeh.server import callbacks\n",
    "output_notebook()\n",
    "\n",
    "def bkapp(doc):\n",
    "\n",
    "    plot = figure(x_range=(-1,1), y_range=(-1,1))\n",
    "    source = ColumnDataSource(df.loc[df.t.eq(0)])    \n",
    "    \n",
    "    def callback(attr, old, new):\n",
    "        source.data = ColumnDataSource.from_df(df.loc[df.t.eq(new)])\n",
    "        \n",
    "    def callback2():\n",
    "        if not button.active:\n",
    "            return\n",
    "        if slider.value <=T_MAX-1:\n",
    "            slider.value += 1\n",
    "        else:\n",
    "            slider.value = 0\n",
    "            \n",
    "    button = Toggle(label=\"Play/Stop\")\n",
    "    \n",
    "    slider = Slider(start=0, end=T_MAX-1, title=\"t\", value=0)\n",
    "    slider.on_change('value', callback)\n",
    "    plot.circle(size=20, radius=0.05, alpha=0.5, source=source, x=\"x1\", y=\"x2\", color=factor_cmap('type', Spectral6, ['Follower', 'Leader']))\n",
    "    layout = Column(slider, button, plot)\n",
    "    \n",
    "    doc.add_root(layout)\n",
    "    doc.add_periodic_callback(callback2, 200)\n",
    "    #curdoc().add_root(layout)\n",
    "    doc.theme = Theme(json=yaml.load(\"\"\"\n",
    "        attrs:\n",
    "            Figure:\n",
    "                background_fill_color: \"#FAFAFA\"\n",
    "                outline_line_color: white\n",
    "                toolbar_location: above\n",
    "                height: 500\n",
    "                width: 500\n",
    "            Grid:\n",
    "                grid_line_dash: [6, 4]\n",
    "                grid_line_color: white\n",
    "    \"\"\", Loader=yaml.FullLoader))\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "6c3fee9e-04fa-408c-b336-8a18a7bbd1d5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.bokehjs_exec.v0+json": "",
      "text/html": [
       "\n",
       "<script id=\"1003\">\n",
       "  (function() {\n",
       "    const xhr = new XMLHttpRequest()\n",
       "    xhr.responseType = 'blob';\n",
       "    xhr.open('GET', \"http://localhost:53685/autoload.js?bokeh-autoload-element=1003&bokeh-absolute-url=http://localhost:53685&resources=none\", true);\n",
       "    \n",
       "    xhr.onload = function (event) {\n",
       "      const script = document.createElement('script');\n",
       "      const src = URL.createObjectURL(event.target.response);\n",
       "      script.src = src;\n",
       "      document.body.appendChild(script);\n",
       "    };\n",
       "    xhr.send();\n",
       "  })();\n",
       "</script>"
      ]
     },
     "metadata": {
      "application/vnd.bokehjs_exec.v0+json": {
       "server_id": "3cb9876043b6414d8960b3a827f51c4c"
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df = run(force=random)\n",
    "show(bkapp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ff4c2bae-7b32-4a8e-9acb-a643ba457742",
   "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}