From 3ad8aa1c98cf28d8f8c8e3eb67209aec92825c0f Mon Sep 17 00:00:00 2001
From: chzhang <zch921005@126.com>
Date: Sun, 11 Dec 2022 17:46:59 +0800
Subject: maze env

---
 rl/tutorials/03_maze.ipynb | 8636 ++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 8636 insertions(+)
 create mode 100644 rl/tutorials/03_maze.ipynb

(limited to 'rl/tutorials/03_maze.ipynb')

diff --git a/rl/tutorials/03_maze.ipynb b/rl/tutorials/03_maze.ipynb
new file mode 100644
index 0000000..17970a7
--- /dev/null
+++ b/rl/tutorials/03_maze.ipynb
@@ -0,0 +1,8636 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 95,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2022-12-11T08:44:34.417254Z",
+     "start_time": "2022-12-11T08:44:34.413619Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "%matplotlib inline"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 1. rendering & visiualization"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 102,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2022-12-11T09:21:03.110244Z",
+     "start_time": "2022-12-11T09:21:02.795689Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "image/png": "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\n",
+      "text/plain": [
+       "<Figure size 360x360 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "fig = plt.figure(figsize=(5, 5))\n",
+    "ax = plt.gca()\n",
+    "ax.set_xlim(0, 3)\n",
+    "ax.set_ylim(0, 3)\n",
+    "\n",
+    "# plt.plot([1, 1], [0, 1], color='red', linewidth=2)\n",
+    "# plt.plot([1, 2], [2, 2], color='red', linewidth=2)\n",
+    "# plt.plot([2, 2], [2, 1], color='red', linewidth=2)\n",
+    "# plt.plot([2, 3], [1, 1], color='red', linewidth=2)\n",
+    "\n",
+    "plt.plot([2, 3], [1, 1], color='red', linewidth=2)\n",
+    "plt.plot([0, 1], [1, 1], color='red', linewidth=2)\n",
+    "plt.plot([1, 1], [1, 2], color='red', linewidth=2)\n",
+    "plt.plot([1, 2], [2, 2], color='red', linewidth=2)\n",
+    "\n",
+    "plt.text(0.5, 2.5, 'S0', size=14, ha='center')\n",
+    "plt.text(1.5, 2.5, 'S1', size=14, ha='center')\n",
+    "plt.text(2.5, 2.5, 'S2', size=14, ha='center')\n",
+    "plt.text(0.5, 1.5, 'S3', size=14, ha='center')\n",
+    "plt.text(1.5, 1.5, 'S4', size=14, ha='center')\n",
+    "plt.text(2.5, 1.5, 'S5', size=14, ha='center')\n",
+    "plt.text(0.5, 0.5, 'S6', size=14, ha='center')\n",
+    "plt.text(1.5, 0.5, 'S7', size=14, ha='center')\n",
+    "plt.text(2.5, 0.5, 'S8', size=14, ha='center')\n",
+    "plt.text(0.5, 2.3, 'START', ha='center')\n",
+    "plt.text(2.5, 0.3, 'GOAL', ha='center')\n",
+    "# plt.axis('off')\n",
+    "plt.tick_params(axis='both', which='both', \n",
+    "                bottom=False, top=False, \n",
+    "                right=False, left=False,\n",
+    "                labelbottom=False, labelleft=False\n",
+    "               )\n",
+    "line, = ax.plot([0.5], [2.5], marker='o', color='g', markersize=60)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 2. agent action policy"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "- $\\pi_\\theta(s,a)$\n",
+    "    - $s: S_0 \\rightarrow S_8$, discrete & finite (3*3, grid world)\n",
+    "    - $a: [0, 1, 2, 3]$, $\\uparrow, \\rightarrow, \\downarrow, \\leftarrow$\n",
+    "    - representation\n",
+    "        - function：nn\n",
+    "        - table：state*action matrix, 每一行表示概率分布（关于动作选择）"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 103,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2022-12-11T09:26:48.437168Z",
+     "start_time": "2022-12-11T09:26:48.431231Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "# border & barrier\n",
+    "theta_0 = np.asarray([[np.nan, 1, 1, np.nan],      # s0\n",
+    "                      [np.nan, 1, np.nan, 1],      # s1\n",
+    "                      [np.nan, np.nan, 1, 1],      # s2\n",
+    "                      [1, np.nan, np.nan, np.nan], # s3 \n",
+    "                      [np.nan, 1, 1, np.nan],      # s4\n",
+    "                      [1, np.nan, np.nan, 1],      # s5\n",
+    "                      [np.nan, 1, np.nan, np.nan], # s6 \n",
+    "                      [1, 1, np.nan, 1]]           # s7\n",
+    "                     )"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 108,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2022-12-11T09:28:48.961283Z",
+     "start_time": "2022-12-11T09:28:48.958093Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "def cvt_theta_0_to_pi(theta):\n",
+    "    m, n = theta.shape\n",
+    "    pi = np.zeros((m, n))\n",
+    "    for r in range(m):\n",
+    "        pi[r, :] = theta[r, :] / np.nansum(theta[r, :])\n",
+    "    return np.nan_to_num(pi)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 109,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2022-12-11T09:28:50.525949Z",
+     "start_time": "2022-12-11T09:28:50.519446Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "pi = cvt_theta_0_to_pi(theta_0)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 110,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2022-12-11T09:28:51.621474Z",
+     "start_time": "2022-12-11T09:28:51.615748Z"
+    },
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[0.        , 0.5       , 0.5       , 0.        ],\n",
+       "       [0.        , 0.5       , 0.        , 0.5       ],\n",
+       "       [0.        , 0.        , 0.5       , 0.5       ],\n",
+       "       [1.        , 0.        , 0.        , 0.        ],\n",
+       "       [0.        , 0.5       , 0.5       , 0.        ],\n",
+       "       [0.5       , 0.        , 0.        , 0.5       ],\n",
+       "       [0.        , 1.        , 0.        , 0.        ],\n",
+       "       [0.33333333, 0.33333333, 0.        , 0.33333333]])"
+      ]
+     },
+     "execution_count": 110,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pi"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 111,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2022-12-11T09:30:45.426920Z",
+     "start_time": "2022-12-11T09:30:45.424159Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "actions = list(range(4))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 112,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2022-12-11T09:30:49.506903Z",
+     "start_time": "2022-12-11T09:30:49.502431Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[0, 1, 2, 3]"
+      ]
+     },
+     "execution_count": 112,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "actions"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 113,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2022-12-11T09:32:55.139792Z",
+     "start_time": "2022-12-11T09:32:55.136071Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "def step(state, action):\n",
+    "    if action == 0:\n",
+    "        state -= 3\n",
+    "    elif action == 1:\n",
+    "        state += 1\n",
+    "    elif action == 2:\n",
+    "        state += 3\n",
+    "    elif action == 3:\n",
+    "        state -= 1\n",
+    "    return state"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 130,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2022-12-11T09:42:39.137272Z",
+     "start_time": "2022-12-11T09:42:39.129306Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "57"
+      ]
+     },
+     "execution_count": 130,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "state = 0\n",
+    "action_history = []\n",
+    "state_history = [state]\n",
+    "while True:\n",
+    "    action = np.random.choice(actions, p=pi[state, :])\n",
+    "    state = step(state, action)\n",
+    "    if state == 8:\n",
+    "        state_history.append(8)\n",
+    "        break\n",
+    "    action_history.append(action)\n",
+    "    state_history.append(state)\n",
+    "len(action_history)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 123,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2022-12-11T09:36:48.886445Z",
+     "start_time": "2022-12-11T09:36:48.882382Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[0, 1, 2, 5, 4, 7, 4, 7]"
+      ]
+     },
+     "execution_count": 123,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "state_history"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 3. rendering & animation"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 124,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2022-12-11T09:37:33.009824Z",
+     "start_time": "2022-12-11T09:37:33.007270Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "from matplotlib import animation\n",
+    "from IPython.display import HTML"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 131,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2022-12-11T09:42:44.836618Z",
+     "start_time": "2022-12-11T09:42:44.832263Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "def init():\n",
+    "    line.set_data([], [])\n",
+    "    return (line, )\n",
+    "def animate(i):\n",
+    "    state = state_history[i]\n",
+    "    x = (state % 3)+0.5\n",
+    "    y = 2.5 - int(state/3)\n",
+    "    line.set_data(x, y)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 132,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2022-12-11T09:42:46.272208Z",
+     "start_time": "2022-12-11T09:42:46.269013Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "anim = animation.FuncAnimation(fig, animate, init_func=init, frames=len(state_history), interval=200, repeat=False)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 128,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2022-12-11T09:41:12.305920Z",
+     "start_time": "2022-12-11T09:41:11.408754Z"
+    }
+   },
+   "outputs": [],
+   "source": [
+    "anim.save('maze_0.mp4')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 133,
+   "metadata": {
+    "ExecuteTime": {
+     "end_time": "2022-12-11T09:42:53.759022Z",
+     "start_time": "2022-12-11T09:42:49.072143Z"
+    }
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "<link rel=\"stylesheet\"\n",
+       "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/\n",
+       "css/font-awesome.min.css\">\n",
+       "<script language=\"javascript\">\n",
+       "  function isInternetExplorer() {\n",
+       "    ua = navigator.userAgent;\n",
+       "    /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
+       "    return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
+       "  }\n",
+       "\n",
+       "  /* Define the Animation class */\n",
+       "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
+       "    this.img_id = img_id;\n",
+       "    this.slider_id = slider_id;\n",
+       "    this.loop_select_id = loop_select_id;\n",
+       "    this.interval = interval;\n",
+       "    this.current_frame = 0;\n",
+       "    this.direction = 0;\n",
+       "    this.timer = null;\n",
+       "    this.frames = new Array(frames.length);\n",
+       "\n",
+       "    for (var i=0; i<frames.length; i++)\n",
+       "    {\n",
+       "     this.frames[i] = new Image();\n",
+       "     this.frames[i].src = frames[i];\n",
+       "    }\n",
+       "    var slider = document.getElementById(this.slider_id);\n",
+       "    slider.max = this.frames.length - 1;\n",
+       "    if (isInternetExplorer()) {\n",
+       "        // switch from oninput to onchange because IE <= 11 does not conform\n",
+       "        // with W3C specification. It ignores oninput and onchange behaves\n",
+       "        // like oninput. In contrast, Mircosoft Edge behaves correctly.\n",
+       "        slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
+       "        slider.setAttribute('oninput', null);\n",
+       "    }\n",
+       "    this.set_frame(this.current_frame);\n",
+       "  }\n",
+       "\n",
+       "  Animation.prototype.get_loop_state = function(){\n",
+       "    var button_group = document[this.loop_select_id].state;\n",
+       "    for (var i = 0; i < button_group.length; i++) {\n",
+       "        var button = button_group[i];\n",
+       "        if (button.checked) {\n",
+       "            return button.value;\n",
+       "        }\n",
+       "    }\n",
+       "    return undefined;\n",
+       "  }\n",
+       "\n",
+       "  Animation.prototype.set_frame = function(frame){\n",
+       "    this.current_frame = frame;\n",
+       "    document.getElementById(this.img_id).src =\n",
+       "            this.frames[this.current_frame].src;\n",
+       "    document.getElementById(this.slider_id).value = this.current_frame;\n",
+       "  }\n",
+       "\n",
+       "  Animation.prototype.next_frame = function()\n",
+       "  {\n",
+       "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
+       "  }\n",
+       "\n",
+       "  Animation.prototype.previous_frame = function()\n",
+       "  {\n",
+       "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
+       "  }\n",
+       "\n",
+       "  Animation.prototype.first_frame = function()\n",
+       "  {\n",
+       "    this.set_frame(0);\n",
+       "  }\n",
+       "\n",
+       "  Animation.prototype.last_frame = function()\n",
+       "  {\n",
+       "    this.set_frame(this.frames.length - 1);\n",
+       "  }\n",
+       "\n",
+       "  Animation.prototype.slower = function()\n",
+       "  {\n",
+       "    this.interval /= 0.7;\n",
+       "    if(this.direction > 0){this.play_animation();}\n",
+       "    else if(this.direction < 0){this.reverse_animation();}\n",
+       "  }\n",
+       "\n",
+       "  Animation.prototype.faster = function()\n",
+       "  {\n",
+       "    this.interval *= 0.7;\n",
+       "    if(this.direction > 0){this.play_animation();}\n",
+       "    else if(this.direction < 0){this.reverse_animation();}\n",
+       "  }\n",
+       "\n",
+       "  Animation.prototype.anim_step_forward = function()\n",
+       "  {\n",
+       "    this.current_frame += 1;\n",
+       "    if(this.current_frame < this.frames.length){\n",
+       "      this.set_frame(this.current_frame);\n",
+       "    }else{\n",
+       "      var loop_state = this.get_loop_state();\n",
+       "      if(loop_state == \"loop\"){\n",
+       "        this.first_frame();\n",
+       "      }else if(loop_state == \"reflect\"){\n",
+       "        this.last_frame();\n",
+       "        this.reverse_animation();\n",
+       "      }else{\n",
+       "        this.pause_animation();\n",
+       "        this.last_frame();\n",
+       "      }\n",
+       "    }\n",
+       "  }\n",
+       "\n",
+       "  Animation.prototype.anim_step_reverse = function()\n",
+       "  {\n",
+       "    this.current_frame -= 1;\n",
+       "    if(this.current_frame >= 0){\n",
+       "      this.set_frame(this.current_frame);\n",
+       "    }else{\n",
+       "      var loop_state = this.get_loop_state();\n",
+       "      if(loop_state == \"loop\"){\n",
+       "        this.last_frame();\n",
+       "      }else if(loop_state == \"reflect\"){\n",
+       "        this.first_frame();\n",
+       "        this.play_animation();\n",
+       "      }else{\n",
+       "        this.pause_animation();\n",
+       "        this.first_frame();\n",
+       "      }\n",
+       "    }\n",
+       "  }\n",
+       "\n",
+       "  Animation.prototype.pause_animation = function()\n",
+       "  {\n",
+       "    this.direction = 0;\n",
+       "    if (this.timer){\n",
+       "      clearInterval(this.timer);\n",
+       "      this.timer = null;\n",
+       "    }\n",
+       "  }\n",
+       "\n",
+       "  Animation.prototype.play_animation = function()\n",
+       "  {\n",
+       "    this.pause_animation();\n",
+       "    this.direction = 1;\n",
+       "    var t = this;\n",
+       "    if (!this.timer) this.timer = setInterval(function() {\n",
+       "        t.anim_step_forward();\n",
+       "    }, this.interval);\n",
+       "  }\n",
+       "\n",
+       "  Animation.prototype.reverse_animation = function()\n",
+       "  {\n",
+       "    this.pause_animation();\n",
+       "    this.direction = -1;\n",
+       "    var t = this;\n",
+       "    if (!this.timer) this.timer = setInterval(function() {\n",
+       "        t.anim_step_reverse();\n",
+       "    }, this.interval);\n",
+       "  }\n",
+       "</script>\n",
+       "\n",
+       "<style>\n",
+       ".animation {\n",
+       "    display: inline-block;\n",
+       "    text-align: center;\n",
+       "}\n",
+       "input[type=range].anim-slider {\n",
+       "    width: 374px;\n",
+       "    margin-left: auto;\n",
+       "    margin-right: auto;\n",
+       "}\n",
+       ".anim-buttons {\n",
+       "    margin: 8px 0px;\n",
+       "}\n",
+       ".anim-buttons button {\n",
+       "    padding: 0;\n",
+       "    width: 36px;\n",
+       "}\n",
+       ".anim-state label {\n",
+       "    margin-right: 8px;\n",
+       "}\n",
+       ".anim-state input {\n",
+       "    margin: 0;\n",
+       "    vertical-align: middle;\n",
+       "}\n",
+       "</style>\n",
+       "\n",
+       "<div class=\"animation\">\n",
+       "  <img id=\"_anim_img4c83f8610e5a427698780d02c9149a43\">\n",
+       "  <div class=\"anim-controls\">\n",
+       "    <input id=\"_anim_slider4c83f8610e5a427698780d02c9149a43\" type=\"range\" class=\"anim-slider\"\n",
+       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
+       "           oninput=\"anim4c83f8610e5a427698780d02c9149a43.set_frame(parseInt(this.value));\"></input>\n",
+       "    <div class=\"anim-buttons\">\n",
+       "      <button onclick=\"anim4c83f8610e5a427698780d02c9149a43.slower()\"><i class=\"fa fa-minus\"></i></button>\n",
+       "      <button onclick=\"anim4c83f8610e5a427698780d02c9149a43.first_frame()\"><i class=\"fa fa-fast-backward\">\n",
+       "          </i></button>\n",
+       "      <button onclick=\"anim4c83f8610e5a427698780d02c9149a43.previous_frame()\">\n",
+       "          <i class=\"fa fa-step-backward\"></i></button>\n",
+       "      <button onclick=\"anim4c83f8610e5a427698780d02c9149a43.reverse_animation()\">\n",
+       "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
+       "      <button onclick=\"anim4c83f8610e5a427698780d02c9149a43.pause_animation()\"><i class=\"fa fa-pause\">\n",
+       "          </i></button>\n",
+       "      <button onclick=\"anim4c83f8610e5a427698780d02c9149a43.play_animation()\"><i class=\"fa fa-play\"></i>\n",
+       "          </button>\n",
+       "      <button onclick=\"anim4c83f8610e5a427698780d02c9149a43.next_frame()\"><i class=\"fa fa-step-forward\">\n",
+       "          </i></button>\n",
+       "      <button onclick=\"anim4c83f8610e5a427698780d02c9149a43.last_frame()\"><i class=\"fa fa-fast-forward\">\n",
+       "          </i></button>\n",
+       "      <button onclick=\"anim4c83f8610e5a427698780d02c9149a43.faster()\"><i class=\"fa fa-plus\"></i></button>\n",
+       "    </div>\n",
+       "    <form action=\"#n\" name=\"_anim_loop_select4c83f8610e5a427698780d02c9149a43\" class=\"anim-state\">\n",
+       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_4c83f8610e5a427698780d02c9149a43\"\n",
+       "             checked>\n",
+       "      <label for=\"_anim_radio1_4c83f8610e5a427698780d02c9149a43\">Once</label>\n",
+       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_4c83f8610e5a427698780d02c9149a43\"\n",
+       "             >\n",
+       "      <label for=\"_anim_radio2_4c83f8610e5a427698780d02c9149a43\">Loop</label>\n",
+       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_4c83f8610e5a427698780d02c9149a43\"\n",
+       "             >\n",
+       "      <label for=\"_anim_radio3_4c83f8610e5a427698780d02c9149a43\">Reflect</label>\n",
+       "    </form>\n",
+       "  </div>\n",
+       "</div>\n",
+       "\n",
+       "\n",
+       "<script language=\"javascript\">\n",
+       "  /* Instantiate the Animation class. */\n",
+       "  /* The IDs given should match those used in the template above. */\n",
+       "  (function() {\n",
+       "    var img_id = \"_anim_img4c83f8610e5a427698780d02c9149a43\";\n",
+       "    var slider_id = \"_anim_slider4c83f8610e5a427698780d02c9149a43\";\n",
+       "    var loop_select_id = \"_anim_loop_select4c83f8610e5a427698780d02c9149a43\";\n",
+       "    var frames = new Array(59);\n",
+       "    \n",
+       "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAWgAAAFoCAYAAAB65WHVAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\\\n",
+       "AAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjEsIGh0\\\n",
+       "dHA6Ly9tYXRwbG90bGliLm9yZy+j8jraAAAcdklEQVR4nO3df3BU9b3/8dcmuyE/Nmn4CmISNMFL\\\n",
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+       "AEMRaAAwFIEGAEMRaAAwFIEGAEMRaAAwFIEGAEMRaAAwFIEGAEMRaAAwFIEGAEMRaAAwFIEGAEMR\\\n",
+       "aAAwFIEGAEMRaAAwFIEGAEMRaAAwFIEGAEMRaAAwFIEGAEMRaAAwFIEGAEMRaAAwFIEGAEMRaAAw\\\n",
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+       "AAAASUVORK5CYII=\\\n",
+       "\"\n",
+       "\n",
+       "\n",
+       "    /* set a timeout to make sure all the above elements are created before\n",
+       "       the object is initialized. */\n",
+       "    setTimeout(function() {\n",
+       "        anim4c83f8610e5a427698780d02c9149a43 = new Animation(frames, img_id, slider_id, 200.0,\n",
+       "                                 loop_select_id);\n",
+       "    }, 0);\n",
+       "  })()\n",
+       "</script>\n"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "execution_count": 133,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "HTML(anim.to_jshtml())"
+   ]
+  },
+  {
+   "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": "3.6.8"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
-- 
cgit v1.2.3