08_gol.ipynb

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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Conway's Game of Life with PySAL"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##Rules##\n",
      "\n",
      "   1. A cell that is currently alive and that has two **or** three live neighbors stays alive\n",
      "   2. A cell that is currently dead with **exactly** three live neighbors comes alive \n",
      "   3. All other cells remain dead, or die due to loneliness (less than 2 neighbors) or overcrowding (more than 3 neighbors)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pysal as ps\n",
      "from scipy.stats import bernoulli"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "k = 8 # dimension of lattice"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "w = ps.lat2W(k,k,rook=False)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "w.n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "64"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "w.neighbors[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "[8, 1, 9]"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "w.neighbors[45]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "[36, 37, 38, 44, 53, 46, 54, 52]"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "w.weights[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "[1.0, 1.0, 1.0]"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y = bernoulli.rvs(0.45,size=w.n)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "array([0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1,\n",
        "       1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1,\n",
        "       0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0])"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "wy = ps.lag_spatial(w,y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "wy"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "array([ 0.,  2.,  1.,  3.,  1.,  2.,  2.,  1.,  0.,  2.,  2.,  5.,  2.,\n",
        "        4.,  3.,  4.,  1.,  3.,  4.,  5.,  4.,  6.,  4.,  3.,  0.,  2.,\n",
        "        2.,  3.,  5.,  4.,  5.,  4.,  2.,  4.,  5.,  4.,  5.,  3.,  5.,\n",
        "        1.,  2.,  3.,  3.,  2.,  3.,  1.,  4.,  2.,  2.,  6.,  5.,  5.,\n",
        "        3.,  3.,  3.,  1.,  2.,  3.,  2.,  3.,  0.,  2.,  1.,  2.])"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "##Rules##\n",
      "\n",
      "   1. A cell that is currently alive and that has two **or** three live neighbors stays alive\n",
      "   2. A cell that is currently dead with **exactly** three live neighbors comes alive \n",
      "   3. All other cells remain dead, or die due to loneliness (less than 2 neighbors) or overcrowding (more than 3 neighbors)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Rule 1: find live cells and count their neighbors"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ywy = y*wy"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "lw23 = np.nonzero( (ywy==2) + (ywy==3) )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "lw23"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "(array([10, 12, 14, 23, 26, 27, 37, 41, 42, 43, 48, 57, 58]),)"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Rule 2: find dead cells with exactly 3 neighbors"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dw3 = (1-y) * wy"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.nonzero(dw3==3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 16,
       "text": [
        "(array([ 3, 17, 44, 52, 53, 54, 59]),)"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Rules 1 and 2 give us the surviving cells"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "live_next = np.nonzero( (ywy==2) + (ywy==3) + (dw3==3) )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "live_next"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 18,
       "text": [
        "(array([ 3, 10, 12, 14, 17, 23, 26, 27, 37, 41, 42, 43, 44, 48, 52, 53, 54,\n",
        "       57, 58, 59]),)"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y[live_next]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "array([0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0])"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So we see that in the future, some dead cells will becoming alive. But what about live cells now that die in the next period?\n",
      "\n",
      "We know that they will be dead next period. Allocate an array with zeros for the next period and assign the live cells. Everyone else is dead."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y1 = np.zeros_like(y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y1[live_next] = 1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 22,
       "text": [
        "array([0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0,\n",
        "       1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0,\n",
        "       0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0])"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "We would then iterate these steps for future generations. \n",
      "\n",
      "Let's place the process inside a function for reuse later"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def generation(y,w):\n",
      "    y1 = np.zeros_like(y)\n",
      "    wy = ps.lag_spatial(w,y)\n",
      "    ywy = y * wy\n",
      "    live_next = np.nonzero( ( ywy == 2 ) + ( ywy == 3 ) + ( ( 1-y ) * wy == 3 ) )\n",
      "    y1[live_next] = 1\n",
      "    return y1\n",
      "        "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 23
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "Try this out on some fresh data."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y = bernoulli.rvs(0.45,size=w.n)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y1 = generation(y,w)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "array([0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1,\n",
        "       0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0,\n",
        "       0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0])"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 27,
       "text": [
        "array([0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0,\n",
        "       1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1,\n",
        "       0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0])"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y2 = generation(y1,w)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 29,
       "text": [
        "array([0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0,\n",
        "       1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0,\n",
        "       1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0])"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "One interesting initial pattern is the so called R-pentomino.\n",
      "\n",
      "We will create one and then run a simulation to see how the solutions evolve."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ngen=350\n",
      "k = 50\n",
      "w = ps.lat2W(k, k, rook=False)\n",
      "#y = bernoulli.rvs(0.45,size=w.n)\n",
      "y = np.zeros((w.n,))\n",
      "#R-pentomino pattern\n",
      "kd2 = k/2\n",
      "top = kd2 +  k * ( kd2 - 1 )\n",
      "topr = top + 1\n",
      "midl = top + k -1\n",
      "mid = midl + 1\n",
      "bot = mid + k\n",
      "y[[top, topr, midl, mid, bot]] = 1\n",
      "results = {}\n",
      "for i in xrange(ngen):\n",
      "    y1 = generation(y,w)\n",
      "    results[i] = y1\n",
      "    if np.all(y == y1):\n",
      "        break\n",
      "    print i, y.sum(), y1.sum()\n",
      "    y = y1\n",
      "    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
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        "170 149.0 167.0\n",
        "171 167.0 135.0\n",
        "172 135.0 157.0\n",
        "173 157.0 148.0\n",
        "174 148.0 157.0\n",
        "175 157.0 160.0\n",
        "176 160.0 162.0\n",
        "177 162.0 163.0\n",
        "178 163.0 142.0\n",
        "179 142.0 156.0\n",
        "180 156.0 152.0\n",
        "181 152.0 157.0\n",
        "182 157.0 152.0\n",
        "183 152.0 144.0\n",
        "184 144.0 148.0\n",
        "185 148.0 152.0\n",
        "186 152.0 156.0\n",
        "187 156.0 151.0\n",
        "188 151.0 156.0\n",
        "189 156.0 144.0\n",
        "190 144.0 135.0\n",
        "191 135.0 141.0\n",
        "192 141.0 145.0\n",
        "193 145.0 146.0\n",
        "194 146.0 162.0\n",
        "195 162.0 148.0\n",
        "196 148.0 155.0\n",
        "197 155.0 133.0\n",
        "198 133.0 169.0\n",
        "199 169.0 140.0\n",
        "200 140.0 146.0\n",
        "201 146.0 142.0\n",
        "202 142.0 122.0\n",
        "203 122.0 124.0\n",
        "204 124.0 119.0\n",
        "205 119.0 130.0\n",
        "206 130.0 127.0\n",
        "207 127.0 129.0\n",
        "208 129.0 113.0\n",
        "209 113.0 106.0\n",
        "210 106.0 110.0\n",
        "211 110.0 108.0\n",
        "212 108.0 109.0\n",
        "213 109.0 112.0\n",
        "214 112.0 120.0\n",
        "215 120.0 99.0\n",
        "216 99.0 112.0\n",
        "217 112.0 100.0\n",
        "218 100.0 107.0\n",
        "219 107.0 102.0\n",
        "220 102.0 104.0\n",
        "221 104.0 102.0\n",
        "222 102.0 116.0\n",
        "223 116.0 88.0\n",
        "224 88.0 89.0\n",
        "225 89.0 93.0\n",
        "226 93.0 95.0\n",
        "227 95.0 94.0\n",
        "228 94.0 92.0\n",
        "229 92.0 98.0\n",
        "230 98.0 83.0\n",
        "231 83.0 94.0\n",
        "232 94.0 74.0\n",
        "233 74.0 77.0\n",
        "234 77.0 75.0\n",
        "235 75.0 79.0\n",
        "236 79.0 82.0\n",
        "237 82.0 74.0\n",
        "238 74.0 86.0\n",
        "239 86.0 67.0\n",
        "240 67.0 67.0\n",
        "241 67.0 59.0\n",
        "242 59.0 61.0\n",
        "243 61.0 65.0\n",
        "244 65.0 62.0\n",
        "245"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " 62.0 68.0\n",
        "246 68.0 64.0\n",
        "247 64.0 75.0\n",
        "248 75.0 70.0\n",
        "249 70.0 73.0\n",
        "250 73.0 69.0\n",
        "251 69.0 79.0\n",
        "252 79.0 67.0\n",
        "253 67.0 71.0\n",
        "254 71.0 66.0\n",
        "255 66.0 66.0\n",
        "256 66.0 58.0\n",
        "257 58.0 60.0\n",
        "258 60.0 57.0\n",
        "259 57.0 58.0\n",
        "260 58.0 63.0\n",
        "261 63.0 62.0\n",
        "262 62.0 73.0\n",
        "263 73.0 66.0\n",
        "264 66.0 78.0\n",
        "265 78.0 75.0\n",
        "266 75.0 73.0\n",
        "267 73.0 79.0\n",
        "268 79.0 84.0\n",
        "269 84.0 93.0\n",
        "270 93.0 88.0\n",
        "271 88.0 86.0\n",
        "272 86.0 85.0\n",
        "273 85.0 84.0\n",
        "274 84.0 78.0\n",
        "275 78.0 71.0\n",
        "276 71.0 62.0\n",
        "277 62.0 63.0\n",
        "278 63.0 64.0\n",
        "279 64.0 72.0\n",
        "280 72.0 62.0\n",
        "281 62.0 55.0\n",
        "282 55.0 56.0\n",
        "283 56.0 54.0\n",
        "284 54.0 47.0\n",
        "285 47.0 48.0\n",
        "286 48.0 42.0\n",
        "287 42.0 42.0\n",
        "288 42.0 41.0\n",
        "289 41.0 39.0\n",
        "290 39.0 39.0\n",
        "291 39.0 39.0\n",
        "292 39.0 39.0\n",
        "293 39.0 39.0\n",
        "294 39.0 39.0\n",
        "295 39.0 39.0\n",
        "296 39.0 39.0\n",
        "297 39.0 39.0\n",
        "298 39.0 39.0\n",
        "299 39.0 39.0\n",
        "300 39.0 39.0\n",
        "301 39.0 39.0\n",
        "302 39.0 39.0\n",
        "303 39.0 39.0\n",
        "304 39.0 39.0\n",
        "305 39.0 39.0\n",
        "306 39.0 39.0\n",
        "307 39.0 39.0\n",
        "308 39.0 39.0\n",
        "309 39.0 39.0\n",
        "310 39.0 39.0\n",
        "311 39.0 39.0\n",
        "312 39.0 39.0\n",
        "313 39.0 39.0\n",
        "314 39.0 39.0\n",
        "315 39.0 39.0\n",
        "316 39.0 39.0\n",
        "317 39.0 39.0\n",
        "318 39.0 39.0\n",
        "319 39.0 39.0\n",
        "320 39.0 39.0\n",
        "321 39.0 39.0\n",
        "322 39.0 39.0\n",
        "323 39.0 39.0\n",
        "324 39.0 39.0\n",
        "325 39.0 39.0\n",
        "326 39.0 39.0\n",
        "327 39.0 39.0\n",
        "328 39.0 39.0\n",
        "329 39.0 39.0\n",
        "330 39.0 39.0\n",
        "331 39.0 39.0\n",
        "332 39.0 39.0\n",
        "333 39.0 39.0\n",
        "334 39.0 39.0\n",
        "335 39.0 39.0\n",
        "336 39.0 39.0\n",
        "337 39.0 39.0\n",
        "338 39.0 39.0\n",
        "339 39.0 39.0\n",
        "340 39.0 39.0\n",
        "341 39.0 39.0\n",
        "342 39.0 39.0\n",
        "343 39.0 39.0\n",
        "344 39.0 39.0\n",
        "345 39.0 39.0\n",
        "346 39.0 39.0\n",
        "347 39.0 39.0\n",
        "348 39.0 39.0\n",
        "349 39.0 39.0\n"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "Create some graphs to look at both the the individual maps  from every 10th generation and then plot the aggregate population size by generation."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "generations = np.zeros((ngen,))\n",
      "living = np.zeros_like(generations)\n",
      "keys = results.keys()\n",
      "keys.sort()\n",
      "for i in keys:\n",
      "    generations[i] = i\n",
      "    living[i] = results[i].sum()\n",
      "    if not i%10:\n",
      "        ymat = results[i]\n",
      "        ymat.shape = (50,50)\n",
      "        imshow(ymat,cmap='Greys', interpolation='nearest')\n",
      "        title(\"Generation %d\"%i)\n",
      "        show()\n",
      "    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x1093a6550>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x109875250>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10955d5d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x109396050>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10788a350>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x109875110>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x109396290>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x109701750>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10788a350>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x107873650>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x109396110>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x109396550>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10788a350>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x109396050>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x109396410>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x109396550>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10938de50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x107873a50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x109396290>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x109396550>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10938de50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x109396050>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x109396110>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x109396550>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10938de50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x109396050>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x109396410>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x109396550>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x107873650>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x109396050>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10938de50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x109396550>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10788a350>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x109396050>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x107873f90>"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "generations.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 32,
       "text": [
        "(350,)"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot(generations,living)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 33,
       "text": [
        "[<matplotlib.lines.Line2D at 0x1098712d0>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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HA//9L11d6RISoi2X4C5i39RE37XWVvebOPZ2OIzjw/T2UimDl1/Wls4NC6N0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\nMD7A/wdScN9MR0tWZQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x109396590>"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ymat = results[ngen-1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ymat.shape"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 35,
       "text": [
        "(2500,)"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ymat.shape=(50,50)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "imshow(ymat, cmap='Greys', interpolation='nearest')\n",
      "title(\"Last Generation\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 37,
       "text": [
        "<matplotlib.text.Text at 0x109887dd0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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jJ1IMoydSDKMnUgyjJ1IMoydSDKMnUgyjJ1IMoydSDKMnUgyjJ1IMoydSDKMnUgyjJ1IM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\nPDw+2AAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10973f5d0>"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ymat = results[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 38
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ymat.shape = (50,50)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 39
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "imshow(ymat, cmap='Greys', interpolation='nearest')\n",
      "title('First Generation: R-pentomino')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 40,
       "text": [
        "<matplotlib.text.Text at 0x1098aa2d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x109565e90>"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 40
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}