Game Of Life Spread of Influence.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Game of Life experiment:\n",
    "\n",
    "1. Set up a Game of Life grid with random cell values {0,1}\n",
    "2. Change the value of a single cell in one of the grids\n",
    "3. Take the difference of the 2 grids and see the extent of the influence of the changed cell\n",
    "\n",
    "On a 256x256 grid the influence speed is linear except for stalls due to static configurations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "71-element Array{Float64,1}:\n",
       "  0.0               \n",
       "  1.4142135623730951\n",
       "  2.8284271247461903\n",
       "  3.6055512754639896\n",
       "  4.47213595499958  \n",
       "  5.656854249492381 \n",
       "  6.4031242374328485\n",
       "  6.708203932499369 \n",
       "  8.06225774829855  \n",
       "  9.433981132056603 \n",
       " 10.295630140987    \n",
       " 11.6619037896906   \n",
       " 12.08304597359457  \n",
       "  ⋮                 \n",
       " 46.95742752749558  \n",
       " 47.4236228055175   \n",
       " 46.95742752749558  \n",
       " 47.4236228055175   \n",
       " 46.95742752749558  \n",
       " 47.4236228055175   \n",
       " 46.95742752749558  \n",
       " 47.4236228055175   \n",
       " 46.95742752749558  \n",
       " 47.4236228055175   \n",
       " 46.95742752749558  \n",
       " 47.4236228055175   "
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = [0.0\n",
    ", 1.4142135623730951\n",
    ", 2.8284271247461903\n",
    ", 3.6055512754639896\n",
    ", 4.47213595499958\n",
    ", 5.656854249492381\n",
    ", 6.4031242374328485\n",
    ", 6.708203932499369\n",
    ", 8.06225774829855\n",
    ", 9.433981132056603\n",
    ", 10.295630140987\n",
    ", 11.6619037896906\n",
    ", 12.08304597359457\n",
    ", 13.453624047073712\n",
    ", 14.317821063276352\n",
    ", 15.620499351813312\n",
    ", 17.029386365926403\n",
    ", 17.804493814764854\n",
    ", 18.439088914585774\n",
    ", 18.439088914585774\n",
    ", 19.849433241279208\n",
    ", 21.2602916254693\n",
    ", 22.022715545545243\n",
    ", 21.93171219946131\n",
    ", 22.022715545545243\n",
    ", 23.08679276123039\n",
    ", 23.40939982143925\n",
    ", 24.698178070456937\n",
    ", 26.0\n",
    ", 27.313000567495326\n",
    ", 28.635642126552703\n",
    ", 29.966648127543394\n",
    ", 29.546573405388315\n",
    ", 29.068883707497267\n",
    ", 30.413812651491096\n",
    ", 30.886890422961002\n",
    ", 31.76476034853718\n",
    ", 33.12099032335839\n",
    ", 33.12099032335839\n",
    ", 34.48187929913334\n",
    ", 35.84689665786985\n",
    ", 37.21558813185679\n",
    ", 38.58756276314948\n",
    ", 38.58756276314948\n",
    ", 39.66106403010388\n",
    ", 39.66106403010388\n",
    ", 41.048751503547585\n",
    ", 42.43819034784589\n",
    ", 43.82921400162225\n",
    ", 43.82921400162225\n",
    ", 43.82921400162225\n",
    ", 43.82921400162225\n",
    ", 44.28317965096905\n",
    ", 44.28317965096905\n",
    ", 45.617978911828175\n",
    ", 46.95742752749558\n",
    ", 47.4236228055175\n",
    ", 46.95742752749558\n",
    ", 47.4236228055175\n",
    ", 46.95742752749558\n",
    ", 47.4236228055175\n",
    ", 46.95742752749558\n",
    ", 47.4236228055175\n",
    ", 46.95742752749558\n",
    ", 47.4236228055175\n",
    ", 46.95742752749558\n",
    ", 47.4236228055175\n",
    ", 46.95742752749558\n",
    ", 47.4236228055175\n",
    ", 46.95742752749558\n",
    ", 47.4236228055175]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "71-element Array{Int64,1}:\n",
       "  1\n",
       "  2\n",
       "  3\n",
       "  4\n",
       "  5\n",
       "  6\n",
       "  7\n",
       "  8\n",
       "  9\n",
       " 10\n",
       " 11\n",
       " 12\n",
       " 13\n",
       "  ⋮\n",
       " 60\n",
       " 61\n",
       " 62\n",
       " 63\n",
       " 64\n",
       " 65\n",
       " 66\n",
       " 67\n",
       " 68\n",
       " 69\n",
       " 70\n",
       " 71"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = collect(1:71)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "using PyPlot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "1-element Array{PyCall.PyObject,1}:\n",
       " PyObject <matplotlib.lines.Line2D object at 0x13a87dc88>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "185-element Array{Float64,1}:\n",
       "  0.0               \n",
       "  1.4142135623730951\n",
       "  2.23606797749979  \n",
       "  2.8284271247461903\n",
       "  3.6055512754639896\n",
       "  5.0               \n",
       "  6.4031242374328485\n",
       "  7.211102550927979 \n",
       "  8.06225774829855  \n",
       "  9.433981132056603 \n",
       " 10.63014581273465  \n",
       " 12.041594578792296 \n",
       " 13.453624047073712 \n",
       "  ⋮                 \n",
       " 91.02197536858888  \n",
       " 90.42676594902639  \n",
       " 91.02197536858888  \n",
       " 90.42676594902639  \n",
       " 91.02197536858888  \n",
       " 90.8019823572151   \n",
       " 91.02197536858888  \n",
       " 91.02197536858888  \n",
       " 91.02197536858888  \n",
       " 91.02197536858888  \n",
       " 90.8019823572151   \n",
       " 90.60353193998564  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y = [0.0\n",
    ", 1.4142135623730951\n",
    ", 2.23606797749979\n",
    ", 2.8284271247461903\n",
    ", 3.6055512754639896\n",
    ", 5.0\n",
    ", 6.4031242374328485\n",
    ", 7.211102550927979\n",
    ", 8.06225774829855\n",
    ", 9.433981132056603\n",
    ", 10.63014581273465\n",
    ", 12.041594578792296\n",
    ", 13.453624047073712\n",
    ", 14.866068747318504\n",
    ", 15.620499351813312\n",
    ", 15.811388300841896\n",
    ", 15.620499351813312\n",
    ", 16.64331697709324\n",
    ", 17.4928556845359\n",
    ", 18.35755975068582\n",
    ", 19.313207915827967\n",
    ", 18.973665961010276\n",
    ", 19.723082923316017\n",
    ", 21.095023109728988\n",
    ", 21.633307652783937\n",
    ", 23.021728866442675\n",
    ", 24.413111231467404\n",
    ", 25.80697580112788\n",
    ", 26.400757564888174\n",
    ", 27.459060435491963\n",
    ", 28.425340807103794\n",
    ", 28.425340807103794\n",
    ", 29.1547594742265\n",
    ", 30.413812651491096\n",
    ", 30.886890422961002\n",
    ", 31.38470965295043\n",
    ", 31.76476034853718\n",
    ", 32.2490309931942\n",
    ", 32.2490309931942\n",
    ", 32.449961479175904\n",
    ", 33.060550509633075\n",
    ", 33.28663395418648\n",
    ", 34.20526275297414\n",
    ", 35.4682957019364\n",
    ", 36.400549446402586\n",
    ", 36.400549446402586\n",
    ", 36.76955262170048\n",
    ", 37.48332962798262\n",
    ", 37.53664875824692\n",
    ", 37.53664875824692\n",
    ", 37.53664875824692\n",
    ", 38.2099463490856\n",
    ", 39.319206502674994\n",
    ", 40.01249804748512\n",
    ", 41.04875150354758\n",
    ", 42.04759208325727\n",
    ", 42.1070065428546\n",
    ", 43.0\n",
    ", 44.01136216933078\n",
    ", 45.01110973970759\n",
    ", 46.01086828130937\n",
    ", 47.0\n",
    ", 47.01063709417264\n",
    ", 48.0\n",
    ", 49.01020301937138\n",
    ", 50.00999900019995\n",
    ", 51.03920062069938\n",
    ", 51.478150704935004\n",
    ", 52.46903848937963\n",
    ", 52.46903848937963\n",
    ", 52.46903848937963\n",
    ", 53.23532661682465\n",
    ", 53.36665625650534\n",
    ", 53.36665625650534\n",
    ", 53.36665625650534\n",
    ", 52.63078946776307\n",
    ", 52.63078946776307\n",
    ", 53.600373133029585\n",
    ", 54.12947441089744\n",
    ", 53.85164807134504\n",
    ", 54.12947441089744\n",
    ", 54.3415126767741\n",
    ", 54.571054598569006\n",
    ", 53.85164807134504\n",
    ", 54.12023651093923\n",
    ", 54.12023651093923\n",
    ", 54.12023651093923\n",
    ", 54.589376255824725\n",
    ", 55.32630477449221\n",
    ", 56.435804238089844\n",
    ", 57.55866572463264\n",
    ", 58.54912467321778\n",
    ", 59.53990258641678\n",
    ", 60.40695324215582\n",
    ", 60.415229867972855\n",
    ", 61.18823416311342\n",
    ", 61.40032573203501\n",
    ", 62.28964600958975\n",
    ", 63.28506932918695\n",
    ", 64.1248781675256\n",
    ", 64.53681120105021\n",
    ", 65.5133574166368\n",
    ", 65.5133574166368\n",
    ", 65.5133574166368\n",
    ", 65.5133574166368\n",
    ", 65.5133574166368\n",
    ", 65.5133574166368\n",
    ", 66.09841147864297\n",
    ", 66.09841147864297\n",
    ", 66.2872536767062\n",
    ", 67.08203932499369\n",
    ", 67.26812023536856\n",
    ", 66.91038783328041\n",
    ", 67.67569726275453\n",
    ", 67.72001181334805\n",
    ", 68.00735254367721\n",
    ", 68.00735254367721\n",
    ", 67.18630812896329\n",
    ", 67.67569726275453\n",
    ", 67.11929677819934\n",
    ", 67.7421582177598\n",
    ", 67.7421582177598\n",
    ", 67.67569726275453\n",
    ", 68.9492567037528\n",
    ", 69.57010852370435\n",
    ", 70.83784299369935\n",
    ", 68.62215385719105\n",
    ", 70.0357051795725\n",
    ", 71.44928271158501\n",
    ", 71.50524456289902\n",
    ", 72.83543093852057\n",
    ", 73.53910524340095\n",
    ", 74.24957912338628\n",
    ", 74.96665925596524\n",
    ", 75.66372975210778\n",
    ", 75.74298647399638\n",
    ", 76.48529270389177\n",
    ", 77.89736837660178\n",
    ", 78.49203781276162\n",
    ", 78.56844150166147\n",
    ", 79.98124780221924\n",
    ", 80.72174428244227\n",
    ", 82.13403679352427\n",
    ", 82.87943049997388\n",
    ", 84.29116205154607\n",
    ", 83.4865258589672\n",
    ", 83.86894538504703\n",
    ", 84.64632301523794\n",
    ", 84.81155581640984\n",
    ", 85.60373823613078\n",
    ", 87.00574693662482\n",
    ", 87.61849119906141\n",
    ", 87.80091115700337\n",
    ", 88.23831367382311\n",
    ", 88.40814442120138\n",
    ", 89.02246907382427\n",
    ", 89.02246907382427\n",
    ", 88.86506625215559\n",
    ", 89.20201791439473\n",
    ", 89.81091247727082\n",
    ", 89.81091247727082\n",
    ", 90.27181176868004\n",
    ", 90.42676594902639\n",
    ", 90.60353193998564\n",
    ", 91.21403400793103\n",
    ", 89.02246907382427\n",
    ", 89.40357934669059\n",
    ", 89.40357934669059\n",
    ", 90.0\n",
    ", 90.2108640907513\n",
    ", 90.8019823572151\n",
    ", 91.02197536858888\n",
    ", 90.8019823572151\n",
    ", 91.02197536858888\n",
    ", 90.42676594902639\n",
    ", 91.02197536858888\n",
    ", 90.42676594902639\n",
    ", 91.02197536858888\n",
    ", 90.8019823572151\n",
    ", 91.02197536858888\n",
    ", 91.02197536858888\n",
    ", 91.02197536858888\n",
    ", 91.02197536858888\n",
    ", 90.8019823572151\n",
    ", 90.60353193998564]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Figure(PyObject <Figure size 640x480 with 1 Axes>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "1-element Array{PyCall.PyObject,1}:\n",
       " PyObject <matplotlib.lines.Line2D object at 0x13a8dd400>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(collect(1:length(y)),y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 1.1.0",
   "language": "julia",
   "name": "julia-1.1"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.1.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}