{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>\n",
       "@import url('http://fonts.googleapis.com/css?family=Source+Code+Pro');\n",
       "@import url('http://fonts.googleapis.com/css?family=Vollkorn');\n",
       "@import url('http://fonts.googleapis.com/css?family=Arimo');\n",
       "\n",
       "    div.cell{\n",
       "        width: 850px;\n",
       "        margin-left: 0% !important;\n",
       "        margin-right: auto;\n",
       "    }\n",
       "    div.text_cell code {\n",
       "        background: transparent;\n",
       "        color: #000000;\n",
       "        font-weight: 600;\n",
       "        font-size: 11pt;\n",
       "        font-style: bold;\n",
       "        font-family:  'Source Code Pro', Consolas, monocco, monospace;\n",
       "   }\n",
       "    h1 {\n",
       "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
       "\t}\n",
       "\t\n",
       "    div.input_area {\n",
       "        background: #F6F6F9;\n",
       "        border: 1px solid #586e75;\n",
       "    }\n",
       "\n",
       "    .text_cell_render h1 {\n",
       "        font-weight: 200;\n",
       "        font-size: 30pt;\n",
       "        line-height: 100%;\n",
       "        color:#c76c0c;\n",
       "        margin-bottom: 0.5em;\n",
       "        margin-top: 1em;\n",
       "        display: block;\n",
       "        white-space: wrap;\n",
       "    } \n",
       "    h2 {\n",
       "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
       "    }\n",
       "    .text_cell_render h2 {\n",
       "        font-weight: 200;\n",
       "        font-size: 16pt;\n",
       "        font-style: italic;\n",
       "        line-height: 100%;\n",
       "        color:#c76c0c;\n",
       "        margin-bottom: 0.5em;\n",
       "        margin-top: 1.5em;\n",
       "        display: inline;\n",
       "        white-space: wrap;\n",
       "    } \n",
       "    h3 {\n",
       "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
       "    }\n",
       "    .text_cell_render h3 {\n",
       "        font-weight: 200;\n",
       "        font-size: 14pt;\n",
       "        line-height: 100%;\n",
       "        color:#d77c0c;\n",
       "        margin-bottom: 0.5em;\n",
       "        margin-top: 2em;\n",
       "        display: block;\n",
       "        white-space: nowrap;\n",
       "    }\n",
       "    h4 {\n",
       "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
       "    }\n",
       "    .text_cell_render h4 {\n",
       "        font-weight: 100;\n",
       "        font-size: 14pt;\n",
       "        color:#d77c0c;\n",
       "        margin-bottom: 0.5em;\n",
       "        margin-top: 0.5em;\n",
       "        display: block;\n",
       "        white-space: nowrap;\n",
       "    }\n",
       "    h5 {\n",
       "        font-family: 'Open sans',verdana,arial,sans-serif;\n",
       "    }\n",
       "    .text_cell_render h5 {\n",
       "        font-weight: 200;\n",
       "        font-style: normal;\n",
       "        color: #1d3b84;\n",
       "        font-size: 16pt;\n",
       "        margin-bottom: 0em;\n",
       "        margin-top: 0.5em;\n",
       "        display: block;\n",
       "        white-space: nowrap;\n",
       "    }\n",
       "    div.text_cell_render{\n",
       "        font-family: 'Arimo',verdana,arial,sans-serif;\n",
       "        line-height: 125%;\n",
       "        font-size: 120%;\n",
       "        width:740px;\n",
       "        margin-left:auto;\n",
       "        margin-right:auto;\n",
       "        text-align:justify;\n",
       "        text-justify:inter-word;\n",
       "    }\n",
       "    div.output_subarea.output_text.output_pyout {\n",
       "        overflow-x: auto;\n",
       "        overflow-y: scroll;\n",
       "        max-height: 50000px;\n",
       "    }\n",
       "    div.output_subarea.output_stream.output_stdout.output_text {\n",
       "        overflow-x: auto;\n",
       "        overflow-y: scroll;\n",
       "        max-height: 50000px;\n",
       "    }\n",
       "    div.output_wrapper{\n",
       "        margin-top:0.2em;\n",
       "        margin-bottom:0.2em;\n",
       "}\n",
       "\n",
       "    code{\n",
       "      font-size: 70%;\n",
       "    }\n",
       "    .rendered_html code{\n",
       "    background-color: transparent;\n",
       "    }\n",
       "    ul{\n",
       "        margin: 2em;\n",
       "    }\n",
       "    ul li{\n",
       "        padding-left: 0.5em; \n",
       "        margin-bottom: 0.5em; \n",
       "        margin-top: 0.5em; \n",
       "    }\n",
       "    ul li li{\n",
       "        padding-left: 0.2em; \n",
       "        margin-bottom: 0.2em; \n",
       "        margin-top: 0.2em; \n",
       "    }\n",
       "    ol{\n",
       "        margin: 2em;\n",
       "    }\n",
       "    ol li{\n",
       "        padding-left: 0.5em; \n",
       "        margin-bottom: 0.5em; \n",
       "        margin-top: 0.5em; \n",
       "    }\n",
       "    ul li{\n",
       "        padding-left: 0.5em; \n",
       "        margin-bottom: 0.5em; \n",
       "        margin-top: 0.2em; \n",
       "    }\n",
       "    a:link{\n",
       "       font-weight: bold;\n",
       "       color:#447adb;\n",
       "    }\n",
       "    a:visited{\n",
       "       font-weight: bold;\n",
       "       color: #1d3b84;\n",
       "    }\n",
       "    a:hover{\n",
       "       font-weight: bold;\n",
       "       color: #1d3b84;\n",
       "    }\n",
       "    a:focus{\n",
       "       font-weight: bold;\n",
       "       color:#447adb;\n",
       "    }\n",
       "    a:active{\n",
       "       font-weight: bold;\n",
       "       color:#447adb;\n",
       "    }\n",
       "    .rendered_html :link {\n",
       "       text-decoration: underline; \n",
       "    }\n",
       "    .rendered_html :hover {\n",
       "       text-decoration: none; \n",
       "    }\n",
       "    .rendered_html :visited {\n",
       "      text-decoration: none;\n",
       "    }\n",
       "    .rendered_html :focus {\n",
       "      text-decoration: none;\n",
       "    }\n",
       "    .rendered_html :active {\n",
       "      text-decoration: none;\n",
       "    }\n",
       "    .warning{\n",
       "        color: rgb( 240, 20, 20 )\n",
       "    } \n",
       "    hr {\n",
       "      color: #f3f3f3;\n",
       "      background-color: #f3f3f3;\n",
       "      height: 1px;\n",
       "    }\n",
       "    blockquote{\n",
       "      display:block;\n",
       "      background: #fcfcfc;\n",
       "      border-left: 5px solid #c76c0c;\n",
       "      font-family: 'Open sans',verdana,arial,sans-serif;\n",
       "      width:680px;\n",
       "      padding: 10px 10px 10px 10px;\n",
       "      text-align:justify;\n",
       "      text-justify:inter-word;\n",
       "      }\n",
       "      blockquote p {\n",
       "        margin-bottom: 0;\n",
       "        line-height: 125%;\n",
       "        font-size: 100%;\n",
       "      }\n",
       "</style>\n",
       "<script>\n",
       "    MathJax.Hub.Config({\n",
       "                        TeX: {\n",
       "                           extensions: [\"AMSmath.js\"]\n",
       "                           },\n",
       "                tex2jax: {\n",
       "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
       "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
       "                },\n",
       "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
       "                \"HTML-CSS\": {\n",
       "                    scale:85,\n",
       "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
       "                }\n",
       "        });\n",
       "</script>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from __future__ import division, print_function\n",
    "%matplotlib inline\n",
    "import sys\n",
    "sys.path.insert(0,'..') # allow us to format the book\n",
    "sys.path.insert(0,'../code') \n",
    "# use same formatting as rest of book so that the plots are\n",
    "# consistant with that look and feel.\n",
    "import book_format\n",
    "book_format.load_style(directory='..')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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2OzReLi8rsyBy7AScAXN3fMpCTk0Ay0kQz32+LWWOyrIEQ6YuSGnzDipDSN0l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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x5a2cda0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from random import uniform\n",
    "import matplotlib.pylab as pylab\n",
    "from matplotlib import animation\n",
    "from gif_animate import animate\n",
    "import matplotlib as mpl\n",
    "from math import pi\n",
    "\n",
    "def make_particle():\n",
    "    return  [uniform(0,100), uniform(0,100), uniform(0, 2), uniform(0, 2*pi)]\n",
    "\n",
    "\n",
    "def move(particles, t=1.):\n",
    "    vx = particles[:, 2]*np.cos(particles[:, 3])\n",
    "    vy = particles[:, 2]*np.sin(particles[:, 3])\n",
    "    particles[:, 0] = (particles[:, 0] + vx*t) % 100\n",
    "    particles[:, 1] = (particles[:, 1] + vy*t) % 100\n",
    "        \n",
    "particles = np.asarray([make_particle() for i in range(1000)])\n",
    "\n",
    "def panimate(frame):\n",
    "    move(particles, t=1.)\n",
    "\n",
    "    plt.cla()\n",
    "    plt.scatter(particles[:, 0], particles[:, 1])\n",
    "    plt.xlim(0, 100)\n",
    "    plt.ylim(0, 100)\n",
    "    plt.gca().get_xaxis().set_ticks([])\n",
    "    plt.gca().get_yaxis().set_ticks([])\n",
    "\n",
    "    \n",
    "animate('13_particle_move.gif', panimate, \n",
    "        frames=500, interval=50, figsize=(4, 4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "<img src='13_particle_move.gif'>"
   ]
  }
 ],
 "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": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}