sierpinski.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Randomly Sierpinski\n",
    "\n",
    "This example is based on a [blog post from John D. Cook](https://www.johndcook.com/blog/2017/07/08/the-chaos-game-and-the-sierpinski-triangle/).\n",
    "\n",
    "I couldn't resist writing a version in a more NumPy-ish style."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def midpoint(*args):\n",
    "    return np.mean(args, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.5      , 0.8660254])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Three corners of an equilateral triangle\n",
    "corner = np.array([(0, 0), (0.5, np.sqrt(3)/2), (1, 0)])\n",
    "corner[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 1000\n",
    "p = np.zeros((N, 2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.25     , 0.4330127])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p[0] = midpoint(corner[0], corner[1])\n",
    "p[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "ks = np.random.choice(3, 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i, k in enumerate(ks):\n",
    "    p[i] = midpoint(p[i-1], corner[k])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "xs, ys = np.transpose(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(xs, ys, s=1)\n",
    "plt.axis([-0.1, 1.1, -0.1, 0.95])\n",
    "plt.xticks([])\n",
    "plt.yticks([])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "points_per_step = 10\n",
    "steps = len(p) // points_per_step"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "%%capture\n",
    "fig, ax = plt.subplots()\n",
    "ax.axis([-0.1, 1.1, -0.1, 1.1])\n",
    "plt.xticks([])\n",
    "plt.yticks([])\n",
    "scatter = ax.scatter([],[], s=2)\n",
    "\n",
    "def animate(i):\n",
    "    scatter.set_offsets(p[:i*points_per_step])\n",
    "\n",
    "from matplotlib.animation import FuncAnimation\n",
    "anim = FuncAnimation(fig, animate, frames=steps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "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",
       "  /* 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",
       "    document.getElementById(this.slider_id).max = this.frames.length - 1;\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",
       "<div class=\"animation\" align=\"center\">\n",
       "    <img id=\"_anim_img99c24f9fa2ab487191febaab1b23863d\">\n",
       "    <br>\n",
       "    <input id=\"_anim_slider99c24f9fa2ab487191febaab1b23863d\" type=\"range\" style=\"width:350px\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           onchange=\"anim99c24f9fa2ab487191febaab1b23863d.set_frame(parseInt(this.value));\"></input>\n",
       "    <br>\n",
       "    <button onclick=\"anim99c24f9fa2ab487191febaab1b23863d.slower()\"><i class=\"fa fa-minus\"></i></button>\n",
       "    <button onclick=\"anim99c24f9fa2ab487191febaab1b23863d.first_frame()\"><i class=\"fa fa-fast-backward\">\n",
       "        </i></button>\n",
       "    <button onclick=\"anim99c24f9fa2ab487191febaab1b23863d.previous_frame()\">\n",
       "        <i class=\"fa fa-step-backward\"></i></button>\n",
       "    <button onclick=\"anim99c24f9fa2ab487191febaab1b23863d.reverse_animation()\">\n",
       "        <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "    <button onclick=\"anim99c24f9fa2ab487191febaab1b23863d.pause_animation()\"><i class=\"fa fa-pause\">\n",
       "        </i></button>\n",
       "    <button onclick=\"anim99c24f9fa2ab487191febaab1b23863d.play_animation()\"><i class=\"fa fa-play\"></i>\n",
       "        </button>\n",
       "    <button onclick=\"anim99c24f9fa2ab487191febaab1b23863d.next_frame()\"><i class=\"fa fa-step-forward\">\n",
       "        </i></button>\n",
       "    <button onclick=\"anim99c24f9fa2ab487191febaab1b23863d.last_frame()\"><i class=\"fa fa-fast-forward\">\n",
       "        </i></button>\n",
       "    <button onclick=\"anim99c24f9fa2ab487191febaab1b23863d.faster()\"><i class=\"fa fa-plus\"></i></button>\n",
       "  <form action=\"#n\" name=\"_anim_loop_select99c24f9fa2ab487191febaab1b23863d\" class=\"anim_control\">\n",
       "    <input type=\"radio\" name=\"state\"\n",
       "           value=\"once\" > Once </input>\n",
       "    <input type=\"radio\" name=\"state\"\n",
       "           value=\"loop\" checked> Loop </input>\n",
       "    <input type=\"radio\" name=\"state\"\n",
       "           value=\"reflect\" > Reflect </input>\n",
       "  </form>\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",
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       "    var slider_id = \"_anim_slider99c24f9fa2ab487191febaab1b23863d\";\n",
       "    var loop_select_id = \"_anim_loop_select99c24f9fa2ab487191febaab1b23863d\";\n",
       "    var frames = new Array(0);\n",
       "    \n",
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