FIZ371_LN47_EST_CellularAutomata_GameOfLife.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cellular Automata\n",
    "**FIZ371 - Scientific & Technical Computations | 12/05/2020**\n",
    "\n",
    "**Game of Life & Cellular Automata**\n",
    "* Introduction\n",
    "* The Rules\n",
    "* Applications\n",
    "* Characteristics\n",
    "* Implementation\n",
    "  * 1-Dimensional\n",
    "    * The Rule\n",
    "  * 2-Dimensional\n",
    "* Classification of Systems\n",
    "* References & Links\n",
    "  \n",
    "Dr. Emre S. Tasci <emre.tasci@hacettepe.edu.tr>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction\n",
    "\n",
    "Towards the end of the 60s, mathematician John H. Conway, after careful considerations, devised a set of simple rules that could mimic complex behaviour depending on the starting conditions. It was made famous after being reported by Martin Gardner on Scientific American (1970) and influenced many people from Richard Feynman to -and especially- Stephen Wolfram."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Rules\n",
    "The rules of the game is simple enough: You start with a graph paper, grid page and fill in some of the boxes as you see fit. This is your starting state. Then for each one of the boxes, depending on the state of its surrounding neighbours (the 4 principal directions for the [von Neumann neighbourhood](https://en.wikipedia.org/wiki/Von_Neumann_neighborhood) and that plus the diagonals for the more commonly used [Moore neighbourhood](https://en.wikipedia.org/wiki/Moore_neighborhood)).\n",
    "\n",
    "Considering the Moore neighbourhood:\n",
    "1. a \"living\" (meaning _filled_) box dies if it has less than 2 or more than 3 living neighbours\n",
    "2. a box becomes \"alive\" if it has exactly 3 living neighbours.\n",
    "\n",
    "This rule set is summarized as \"B3/S23\" (as in: \"Born @ 3 / Survives @ 2 or 3\")."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Applications\n",
    "There are many implementations of these rules. Most succesful among them being:\n",
    "1. https://copy.sh/life/\n",
    "2. http://pmav.eu/stuff/javascript-game-of-life-v3.1.1/\n",
    "\n",
    "[A dedicated wiki](https://www.conwaylife.com/wiki/Main_Page) about almost anything related to the \"Game of Life\" is also available via the https://www.conwaylife.com/ site. For instance, some examples of specific behaviour clusters are:\n",
    "1. [Still Lives](http://www.conwaylife.com/wiki/List_of_common_still_lives)\n",
    "2. [Oscillators](http://www.conwaylife.com/wiki/List_of_common_oscillators)\n",
    "3. [Space Ships](http://www.conwaylife.com/wiki/List_of_spaceships)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Characteristics\n",
    "It has been proven that \"Game of Life\" system is Turing complete (meaning that, it can be programmed to construct itself and/or variants _(or anything)_), i.e., a universal machine. Stephen Wolfram has played a huge role in the said proof [*](https://mathworld.wolfram.com/GameofLife.html). \n",
    "\n",
    "Wolfram believed -and still believes- that our universe can be understood as a similar automaton, obeying a set of simple rules like those of the Game of Life. Very recently (a month ago of this writing: April 14th, 2020), [he announced that he had achieved kind of a breakthrough in his quest to explain the physical laws via automatons(https://writings.stephenwolfram.com/2020/04/finally-we-may-have-a-path-to-the-fundamental-theory-of-physics-and-its-beautiful/)]. Coincidentally, his announcement took place just 3 days after [John Conway passed away on the 11th](https://www.dailyprincetonian.com/article/2020/04/john-conway-dead-covid-19), at the age of 82 due to Covid 19 related issues."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Implementation\n",
    "Game of Life has many different variations with respect to its set of rules and/or dimensions but the standard is B3/S23 on a 2D square grid, using the Moore neighbourhood. There are many implementations available on the web, but to understand the process we will start by implementing a 1D version so that we can also understand the classifications with respect to the specified rules, and then will move on to the standard, 2D version."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1-Dimensional\n",
    "When you are living in a 1D universe, you'll have 2 immediate neighbours: one to your left and the other to your right, so at any time, we will be focusing (doing calculations) on 3 consecutive boxes. As each of the boxes can be in one of the 2 states (being 'dead' or 'alive'), there are a total of 8 possible outcomes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\t000\t◻◻◻\n",
      "1\t001\t◻◻◼\n",
      "2\t010\t◻◼◻\n",
      "3\t011\t◻◼◼\n",
      "4\t100\t◼◻◻\n",
      "5\t101\t◼◻◼\n",
      "6\t110\t◼◼◻\n",
      "7\t111\t◼◼◼\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "for state in range(8):\n",
    "    state_2 = np.base_repr(state,base=2)\n",
    "    print(\"{:d}\\t{:0>3s}\\t{:s}\".format(state,state_2,\n",
    "       \"{:0>3s}\".format(state_2).replace(\"0\",\"◻\").replace(\"1\",\"◼\")))\n",
    "    #world_t_str = ''.join(world[0,:].astype(str))\n",
    "#world_t_str_symb = world_t_str.replace(\"0\",\"◻\").replace(\"1\",\"◼\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Rule\n",
    "The rule defines what happens to the cell in the middle at the next turn -- it can:\n",
    "1. Keep on being what it was (dead -> dead | alive -> alive)\n",
    "2. Go to the opposite state (dead -> alive | alive -> dead)\n",
    "3. Die ({dead, alive} -> dead)\n",
    "4. Become alive ({dead,alive} -> alive)\n",
    "\n",
    "Let's impose a set of rules of our own - it should cover all of the 8 possible states, so let it be something like:\n",
    "\n",
    "state|binary|representation|$\\rightarrow$|outcome|representation\n",
    "---|---|---|---|---|---\n",
    "7|111|◼◼◼ |$\\rightarrow$|0|◻\n",
    "6|110|◼◼◻ |$\\rightarrow$|1|◼\n",
    "5|101|◼◻◼ |$\\rightarrow$|0|◻\n",
    "4|100|◼◻◻ |$\\rightarrow$|1|◼\n",
    "3|011|◻◼◼ |$\\rightarrow$|1|◼\n",
    "2|010|◻◼◻ |$\\rightarrow$|0|◻\n",
    "1|001|◻◻◼ |$\\rightarrow$|1|◼\n",
    "0|000|◻◻◻ |$\\rightarrow$|0|◻\n",
    "\n",
    "By ordering this rule like this, from 111 to 000, we write the corresponding outcomes side by side, i.e., \"01011010\", then for practicality and mnemonic reasons, we treat this set of outcomes as if it is a binary number and convert it to the decimal system:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "90"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "int(\"01011010\",2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "thus, our rule as specified above is referred as \"[rule 90](https://www.wolframalpha.com/input/?i=rule+90)\". Let's see this rule at work, for a random starting configuration:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
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   "source": [
    "\"\"\"\n",
    "/* Emre S. Tasci <emre.tasci@hacettepe.edu.tr>          *\n",
    "*\n",
    "* Filename: game_of_life_1D.m\n",
    "*\n",
    "* 1D Game of Life implementation.\n",
    "*\n",
    "* Saves the states in \"aux_aux_world.txt\" (as a matrix) and\n",
    "* \"aux_timeline.txt\" (as visuals).\n",
    "*\n",
    "Rule #90, World Size: 40\n",
    "\n",
    "Initial state:\n",
    "0 0 0 0 0 1 1 0 1 0 1 0 1 0 0 0 1 1 0 1 1 1 0 0 1 0 1 1 1 1 0 0 1 0 1 0 1 0 0 0\n",
    "\n",
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    "000004\t◼◼◻◻◻◼◻◻◻◼◼◻◼◻◻◼◼◼◻◼◻◼◼◻◼◻◼◻◼◻◼◻◻◻◼◻◼◼◼◻\n",
    "000005\t◻◻◻◼◻◼◻◼◻◻◻◼◼◻◻◻◼◻◼◼◼◻◻◼◼◼◼◼◼◼◼◻◼◻◼◼◻◼◻◼\n",
    "000006\t◻◼◻◼◼◼◼◼◻◼◻◻◻◻◼◻◼◼◻◼◻◻◻◻◼◼◼◼◼◼◻◼◼◼◻◻◼◼◼◼\n",
    "000007\t◼◼◼◻◼◼◼◻◼◼◻◼◼◻◼◼◻◻◼◼◻◼◼◻◻◼◼◼◼◻◼◻◼◻◻◻◻◼◼◻\n",
    "000008\t◻◼◻◼◻◼◻◼◻◻◼◻◻◼◻◻◻◻◻◻◼◻◻◻◻◻◼◼◻◼◼◼◼◻◼◼◻◻◻◼\n",
    "000009\t◼◼◼◼◼◼◼◼◻◻◼◻◻◼◻◼◼◼◼◻◼◻◼◼◼◻◻◻◼◻◼◼◻◼◻◻◻◼◻◼\n",
    "000010\t◼◼◼◼◼◼◼◻◻◻◼◻◻◼◼◻◼◼◻◼◼◼◻◼◻◻◼◻◼◼◻◻◼◼◻◼◻◼◼◻\n",
    "\n",
    "*                                             09/12/18 */\n",
    "\"\"\"\n",
    "import numpy as np\n",
    "\n",
    "world_size = 40\n",
    "num_of_time_steps = 50\n",
    "k = 3\n",
    "\n",
    "# Create the world as a num_of_time_steps x world_size size matrix:\n",
    "world = np.zeros([num_of_time_steps,world_size]);\n",
    "\n",
    "def modd(n):\n",
    "    return np.mod(n,world_size)\n",
    "def bin2dec(bin):\n",
    "    return int(bin,2)\n",
    "def dec2bin(dec):\n",
    "    return np.base_repr(dec,base=2)\n",
    "\n",
    "\n",
    "# Define the rules:\n",
    "rules = [None]*8;\n",
    "rules[0] = 0; # 000 => 0\n",
    "rules[1] = 1; # 001 => 1\n",
    "rules[2] = 0; # 010 => 0\n",
    "rules[3] = 1; # 011 => 1\n",
    "rules[4] = 1; # 100 => 1\n",
    "rules[5] = 0; # 101 => 0\n",
    "rules[6] = 1; # 110 => 1\n",
    "rules[7] = 0; # 111 => 0\n",
    "\n",
    "world = np.zeros([num_of_time_steps,world_size],int)\n",
    "#print(world.shape)\n",
    "\n",
    "file_id = open(\"aux_timeline_py.txt\",\"w\")\n",
    "#file_id.write(\"Rule #%d, World Size: %d\\n\\n\",bin2dec(strrep(num2str(rules),\" \",\"\")),world_size)\n",
    "rule = ''.join(map(str,rules))\n",
    "file_id.write(\"Rule #%d, World Size: %d\\n\\n\"%(bin2dec(rule),world_size))\n",
    "\n",
    "# Define the initial state:\n",
    "# Randomly fill with 0 & 1 of a 1 row, world_size cols sized matrix\n",
    "world[0,:] = np.random.randint(0,2,(1,world_size))\n",
    "file_id.write(\"Initial state:\\n%s\\n\\n\"%(' '.join(world[0,:].astype(str))))\n",
    "world_t_str = ''.join(world[0,:].astype(str))\n",
    "world_t_str_symb = world_t_str.replace(\"1\",\"◻\").replace(\"0\",\"◼\")\n",
    "print(\"%06d\\t%s\\n\"%(1,world_t_str_symb),end=\"\")\n",
    "file_id.write(\"%06d\\t%s\\n\"%(1,world_t_str_symb))\n",
    "\n",
    "for t in range(1,num_of_time_steps):\n",
    "    for n in range(0,world_size):\n",
    "        previous_t_left_neighbor_state= world[t-1,np.mod(n-1,world_size)].astype(str)\n",
    "        previous_t_self_neighbor_state= world[t-1,np.mod(n,world_size)].astype(str)\n",
    "        previous_t_right_neighbor_state= world[t-1,np.mod(n+1,world_size)].astype(str)\n",
    "        previous_t_triple_state = previous_t_left_neighbor_state+previous_t_self_neighbor_state+previous_t_right_neighbor_state\n",
    "        #print(\"%3d\\t%3d\\t%3s\" % (t,n,previous_t_triple_state))\n",
    "        rule = rules[bin2dec(previous_t_triple_state)];\n",
    "        world[t,n] = rule;\n",
    "    world_t_str = ''.join(world[t,:].astype(str))\n",
    "    world_t_str_symb = world_t_str.replace(\"1\",\"◻\").replace(\"0\",\"◼\")\n",
    "    print(\"%06d\\t%s\\n\"%((t+1),world_t_str_symb),end=\"\")\n",
    "    file_id.write(\"%06d\\t%s\\n\"%((t+1),world_t_str_symb))\n",
    "    #printf(figure_form);\n",
    "\n",
    "#print(world)\n",
    "file_id.close()\n",
    "\n",
    "np.savetxt(\"aux_world_py.txt\",world,\"%d\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2-Dimensional"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f61c941c860>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f61c9d12ac8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f61c91d5b70>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f61c98562e8>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f61c9098da0>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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kJgNCUpMBscIlOSLJn4xpWy9Mcm33VO2tSdb2rXt/t/yBJG/qWz7wSdxuXMut3ZOe13ZjXEjy9iR7+p6UfMc4+q7hGBAr3xHAWAICuAh4qqpeCVwOfBige7p2E/Aqek8+/mOSVQd4EvfD9J6IXAc81W17zrV9T0p+ekx91xAMiJXvMuAV3f/GHxlxW/1PZ34JODO9kV4bgWuq6mdV9d/ADnrDjwc+idt95w3dNmBKn/R8Plj2Iyk1skuAV1fV+kErk3wDOHzAqr+sqn+ft+y5J2u7Ea5PAy/pln+7r13/E7fzn8R9bfedH1bV3gHtAX67e3Dt+8CfV1X/NrSEDIjnuap6/UE0bz1Z21o+6Ax1f+0B/g24uqp+luRd9M4u3nAQfdQYGRDPcwd5BjH3ZO1skkOAF9F7mcr+nrgdtPxx4Igkh3RnEc+1r6on+tp/iu4+hybDgFj5fsTgAAAO+gxi7unMbwFvBb5WVZVkK/CFJB8DjgXWAd+hd6awLsmJwCP0bmT+Xvedr3fbuIa+Jz2THDP3khngfOC+g+ifxsyAWOGq6okk/9G9dPX6qvqrETb3GeBzSXbQO3PY1O3j3iRfBL4H7AXeU1XPAuznSdz3Adck+TvgP7ttA/xpkvO77TwJvH2E/mpEPs0pqcmfOSU1GRCSmgwISU0GhKQmA0JSkwEhqcmAkNRkQEhq+j/2owODMw1YiwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f61c9c62320>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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rpUmu656qvS3J6r51H+6WP5TkrX3LBz6J241rua170vO6bozLvnXvTnJ/kvuSfHEcfddwDIjZdwQwloAALgKerqrXApcDHwfonq7dALyO3pOP/5RkxUGexP04vSci1wBPd9smyRrgw/SGob8OeP+Y+q4hGBCz7zLgNd17Cz4x4rb6n878MnBWeiO91gPXVtX/VtX3gR30hh8PfBK3+86bu23A85/0/DPgyqp6Gp4bhq4JWfYjKTWyS4BTqmrtoJVJbgEOH7Dqg1X1H/OWPfdkbTfC9RngqG75rX3t+p+4nf8k7hu67/yoqvYOaP/rXb++TW/k7EeneYTptDMgXuSq6k0voHnrydrW8kFnqAdqD73/JtfQG958PHBLklOq6kcvoJ8aEwPiRe4FnkHse7J2LskhwMvovUzlQE/cDlr+BHBEkkO6s4j+9nPArVX1f8D3kzxELzBuH/IQNQLvQcy+HzM4AIDeGUTfq9P6/80PB3j+05nvBL5RvYd5tgAbul85TqT3f+jv0ngSt/vON7ttwPOf9PwKcCZAkpX0LjkeGfroNRIDYsZV1ZPAt5PcO4ablJ8DjkqyA/gA3Tsmu6drvwTcD1wPvK97X8JeYN+TuA8AX+p7EvdDwAe6bR3VbZuu7ZNJ7qcXIn/dHYMmwKc5JTV5BiGpyYCQ1GRASGoyICQ1GRCSmgwISU0GhKQmA0JS0/8DsdzhCvrrbmwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f61c91b3668>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f61c981b630>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f61c9ab7a58>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f61c9c64940>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f61c9797c88>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\"\"\"\n",
    "/* Emre S. Tasci <emre.tasci@hacettepe.edu.tr>          *\n",
    "*\n",
    "* Filename: game_of_life_2D.m\n",
    "*\n",
    "* 2D Game of Life implementation.\n",
    "*                                             09/12/18 */\n",
    "\"\"\"\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "world_size = {\"x\":0,\"y\":0}\n",
    "world_size[\"x\"] = 20\n",
    "world_size[\"y\"] = 20\n",
    "\n",
    "num_time_steps = 10;\n",
    "#np.arccos()\n",
    "def modd_x(n):\n",
    "    return np.mod(n,world_size[\"x\"])\n",
    "\n",
    "def modd_y(n):\n",
    "    return np.mod(n,world_size[\"y\"])\n",
    "\n",
    "def show_matrix(world,fig,t=0,pause_time=0.5):\n",
    "    #fig = plt.figure()\n",
    "    ax = fig.add_subplot(1, 1, 1)\n",
    "\n",
    "    # Major ticks every 20, minor ticks every 5\n",
    "    major_ticks = np.arange(0.5, world_size[\"x\"] ,1)\n",
    "    minor_ticks = np.arange(0.5, world_size[\"x\"], 1)\n",
    "\n",
    "    ax.set_xticks(major_ticks)\n",
    "    #ax.set_xticks(minor_ticks, minor=True)\n",
    "    ax.set_yticks(major_ticks)\n",
    "    #ax.set_yticks(minor_ticks, minor=True)\n",
    "\n",
    "    # And a corresponding grid\n",
    "    ax.grid(which='both')\n",
    "\n",
    "    # Or if you want different settings for the grids:\n",
    "    #ax.grid(which='minor', alpha=1)\n",
    "    ax.grid(which='major', alpha=1)\n",
    "    ax.set_yticklabels([])\n",
    "    ax.set_xticklabels([])\n",
    "    plt.imshow(world,cmap='Greys')\n",
    "    plt.draw()\n",
    "    plt.xlabel(\"t = %05d\"%t)\n",
    "    #plt.show()\n",
    "    plt.pause(pause_time)\n",
    "    #input(\"...\")\n",
    "    plt.clf()\n",
    "\n",
    "\n",
    "# Random\n",
    "world = np.random.randint(0,2,[world_size[\"y\"], world_size[\"x\"]])\n",
    "\n",
    "# Glider Spaceship (http://www.conwaylife.com/wiki/Glider)\n",
    "world = np.zeros([world_size[\"y\"], world_size[\"x\"]])\n",
    "world[1,2] = world[2,3] = world[3,1:4] = 1\n",
    "\n",
    "# Ligthweight Spaceship (http://www.conwaylife.com/wiki/Lightweight_spaceship\n",
    "world = np.zeros([world_size[\"y\"], world_size[\"x\"]])\n",
    "world[1,2] = world[1,5] = world[2,1] = world[3,1] = world[3,5] = world[4,1:5] = 1\n",
    "\n",
    "# Figure eight (http://www.conwaylife.com/wiki/Figure_eight)\n",
    "world = np.zeros([world_size[\"y\"], world_size[\"x\"]])\n",
    "world[3:6,3:6] = world[6:9,6:9] = 1\n",
    "\n",
    "fig = plt.figure()\n",
    "show_matrix(world,fig)\n",
    "\n",
    "aux = world.copy()\n",
    "#print(world)\n",
    "#print(world.shape)\n",
    "for t in range(0,num_time_steps):\n",
    "    for row in range(0,world_size[\"y\"]):\n",
    "        for col in range(0,world_size[\"x\"]):\n",
    "            # Count the neighbours\n",
    "            neighbours = []\n",
    "            #print(\"(%2d,%2d):\\t\"%(row,col),end=\"\")\n",
    "            for i in range(-1,2):\n",
    "                for j in range(-1,2):\n",
    "                    #if(i == j == 0):\n",
    "                    #    continue\n",
    "                    #print(\"(%d,%d) \"%(modd_y(row+j),modd_x(col+i)),end=\"\")\n",
    "                    neighbours.append(world[modd_y(row+i),modd_x(col+j)])\n",
    "\n",
    "            #print(\"\")\n",
    "            #print(neighbours)\n",
    "            count_neighbours = sum(neighbours) - world[row,col] # Don't count itself as neighbor\n",
    "            if(count_neighbours == 3):\n",
    "                aux[row,col] = 1\n",
    "            elif(count_neighbours == 2):\n",
    "                aux[row,col] = world[row,col]\n",
    "            else:\n",
    "                aux[row,col] = 0\n",
    "    world = aux.copy()\n",
    "    #print(world)\n",
    "    show_matrix(world,fig,t+1,pause_time=0.1)\n",
    "plt.close()"
   ]
  },
  {
   "attachments": {
    "cellular_automata_classification_Wolfram.png": {
     "image/png": 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"
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    "# Classification of Systems\n",
    "[According to the Stephen Wolfram](https://www.wolframscience.com/nks/p231--four-classes-of-behavior/), a celular automata can be classified into one of the following 4 systems:\n",
    "1. Almost all initial conditions lead to exactly the same uniform final state.\n",
    "2. The final state becomes a repetition.\n",
    "3. The evolution seems complicated alas a pattern-like behaviour (such as triangles) emerges.\n",
    "4. Clusters interact with each other to evolve into even complex and evergoing systems.\n",
    "\n",
    "It is this 4th class that is promising.\n",
    "\n",
    "![cellular_automata_classification_Wolfram.png](attachment:cellular_automata_classification_Wolfram.png)\n",
    "Stephen Wolfram, \"A New Kind of Science: Four Classes of Behavior: Image Source for Page 231\" from the Notebook Archive (2018), https://notebookarchive.org/2018-12-1g671ci"
   ]
  },
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   "source": [
    "# References & Links:\n",
    "## Articles\n",
    "* [Martin Gardner, “Mathematical Games: The fantastic combinations of John Conway's new solitaire game ‘life’”, Scientific American 223 120 (1970)](http://dx.doi.org/10.1038)\n",
    "* [Dierk Schleicher, “Interview with John Horton Conway”, Notices of the American Mathematical Society 60 567 (2013)](https://www.ams.org/notices/201305/rnoti-p567.pdf)\n",
    "* [Stephen Wolfram, \"A New Kind of Science\"](https://www.wolframscience.com/nks/)\n",
    "* [Mark Andrew Smith, \"Cellular Automata Methods in Mathematical Physics\", Ph.D. Thesis, MIT (1994)](https://dl.acm.org/doi/pdf/10.5555/888548)\n",
    "* [A.I. Adamatzky, \"Computation of Shortest Path in Cellular Automata\", Mathl. Comput. Modelling (23) 105 (1996)](https://doi.org/10.1016/0895-7177(96)00006-4)\n",
    "## Videos\n",
    "* [Civilization III Summary replay](https://www.youtube.com/watch?v=V7SKQAw7Txw)\n",
    "* [Programmable self-assembly in a thousand-robot swarm](https://www.youtube.com/watch?v=xK54Bu9HFRw)\n",
    "* [World War II in Europe: Every Day](https://www.youtube.com/watch?v=WOVEy1tC7nk)\n",
    "## Implementations\n",
    "* https://copy.sh/life/ (Detailed & complex)\n",
    "* http://pmav.eu/stuff/javascript-game-of-life-v3.1.1/ (simpler)\n",
    "* [Digital clock implementation](https://copy.sh/life/?gist=f3413564b1fa9c69f2bad4b0400b8090&step=512)\n",
    "* [Reaction-Diffusion Simulation using Gray-Scott Model / Karl Sims](http://karlsims.com/rd.html)\n",
    "\n",
    "* [Game of Life Wiki](http://www.conwaylife.com/wiki/Main_Page)\n"
   ]
  },
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   "source": []
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