Explore 1D Cellular Automata in python

Automata.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "850bea27-e241-4a46-aea7-6fa08f28d68e",
   "metadata": {},
   "source": [
    "# [Elementary Cellular automata](https://en.wikipedia.org/wiki/Elementary_cellular_automaton)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9b57a8a5-062b-44ac-852f-b63e88bb96f1",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import PIL.Image\n",
    "from functools import partial"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e25693f-1e1e-46d8-b2af-8402c966c262",
   "metadata": {},
   "source": [
    "## Show an image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ef26abe5-18d3-4ab6-b4e7-fb409ea06dd1",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def show(screen, scale = 8):\n",
    "    return (\n",
    "        PIL.Image.fromarray(screen.astype(np.uint8).T*230, 'L')\n",
    "        .resize((screen.shape[0]*scale,screen.shape[1]*scale), resample=PIL.Image.NEAREST)\n",
    "    )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "b3617c06-6fbc-46e0-afc5-44ebe64403f8",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "width = 32\n",
    "height = 16\n",
    "screen = np.ones((width, height), dtype=np.bool_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "5b46c1b0-4f5b-4044-8aa1-4cbc832f81c9",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "screen[10,5]  = 0\n",
    "screen[14,5]  = 0\n",
    "screen[12,7]  = 0\n",
    "screen[ 9,9]  = 0\n",
    "screen[10,10] = 0\n",
    "screen[11,10] = 0\n",
    "screen[12,10] = 0\n",
    "screen[13,10] = 0\n",
    "screen[14,10] = 0\n",
    "screen[15,9]  = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b47fbeb7-3764-4a27-8be2-042279a5e3af",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<PIL.Image.Image image mode=L size=256x128>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show(screen)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fdb1ebad-71be-41bb-9a32-8054cbf13681",
   "metadata": {},
   "source": [
    "## Manual computation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "e48acf6c-87e6-459e-b382-58535d55f224",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "black = 0\n",
    "white = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "67a15df7-1056-4804-9008-a1ec601450a0",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Initialize\n",
    "width = 256\n",
    "height = width//2\n",
    "screen = np.ones((width, height), dtype=np.bool_)\n",
    "screen[width//2,0] = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "d7e86768-4a11-4fcb-a85a-ada5d12fd877",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<PIL.Image.Image image mode=L size=512x256>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Manually apply rules\n",
    "for line in range(1, height):\n",
    "    for x in range(1, width-1):\n",
    "        if screen[x+1,line-1] == black and screen[x-1,line-1] == black:\n",
    "            screen[x,line] = white\n",
    "        elif screen[x+1,line-1] == black:\n",
    "            screen[x,line] = black\n",
    "        elif screen[x-1,line-1] == black:\n",
    "            screen[x,line] = black\n",
    "        else:\n",
    "            screen[x,line] = white\n",
    "show(screen,scale=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d118de8-666c-4e1a-9f20-71cfa61576c9",
   "metadata": {},
   "source": [
    "## Putting it in a function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "70775d42-ec45-47dc-8cd5-527361714dcc",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def automaton(rule, height=128, random=False):\n",
    "    width = height*2\n",
    "    screen = np.ones((width, height), dtype=np.bool_)\n",
    "    \n",
    "    if random:\n",
    "        # random start\n",
    "        screen[:,0] = np.random.random(width) < 0.5\n",
    "    else:\n",
    "        # Single pixel to start\n",
    "        screen[width//2,0] = 0\n",
    "    \n",
    "    for line in range(1, height):\n",
    "        for x in range(1, width-1):\n",
    "            a = screen[x-1,line-1]\n",
    "            b = screen[x,  line-1]\n",
    "            c = screen[x+1,line-1]\n",
    "            \n",
    "            screen[x, line] = rule(a,b,c)\n",
    "    \n",
    "    return screen"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "46a331a5-fcc2-4112-a253-4344d7634b6e",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<PIL.Image.Image image mode=L size=2048x1024>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Equivalent to manual rule\n",
    "def rule_adrian(a,b,c):\n",
    "    if a == black and c == black:\n",
    "        return white\n",
    "    if a == black:\n",
    "        return black\n",
    "    if c == black:\n",
    "        return black\n",
    "    return white\n",
    "\n",
    "show(automaton(rule_adrian))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "e7061d3a-5cc1-49f8-a46b-cf3e06fcafd7",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<PIL.Image.Image image mode=L size=2048x1024>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show(automaton(rule_adrian, random=True))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "21858001-2751-4372-b7bb-c82fe5b44fca",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<PIL.Image.Image image mode=L size=2048x1024>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def rule90(a,b,c):\n",
    "    if a == c:\n",
    "        return white\n",
    "    return black\n",
    "\n",
    "show(automaton(rule90, random=True))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73200b2f-e948-427e-8a33-0c089186c580",
   "metadata": {},
   "source": [
    "## Decorator version"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "c70276e4-15ad-4a62-9acb-fff23a03102e",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def single_init(width):\n",
    "    line = np.ones(width, dtype=np.bool_)\n",
    "    line[width//2] = 0\n",
    "    return line\n",
    "\n",
    "def rand_init(width):\n",
    "    return np.random.random(width) < 0.5\n",
    "\n",
    "def automaton_rule(rule):\n",
    "    \"\"\"Decorator for 3-bit 1D automata\n",
    "    \n",
    "    Usage:\n",
    "        @automaton_rule\n",
    "        rule(a:bool,b:bool,c:bool) -> bool: ...\n",
    "        \n",
    "    which can then be called like\n",
    "        rule(width, height, init=single_init)\n",
    "    \"\"\"\n",
    "    def wrapped(rule, width=None, height=None, init=single_init):\n",
    "        if width is None:\n",
    "            if height is None:\n",
    "                width = 256\n",
    "            else:\n",
    "                width = height*2\n",
    "        if height is None:\n",
    "            height = width//2\n",
    "\n",
    "        screen = np.zeros((width, height), dtype=np.bool_)\n",
    "\n",
    "        screen[:,0] = init(width)\n",
    "\n",
    "        for line in range(1, height):\n",
    "            for x in range(width):\n",
    "                a = screen[(x-1 )% width,line-1]\n",
    "                b = screen[x,  line-1]\n",
    "                c = screen[(x+1) % width,line-1]\n",
    "\n",
    "                screen[x, line] = rule(a,b,c)\n",
    "\n",
    "        return screen\n",
    "    return partial(wrapped,rule)\n",
    "\n",
    "def show_rule(rule) -> np.array:\n",
    "    \"Returns a small 10x2 array showing all possible bit patterns\"\n",
    "    def init(width):\n",
    "        return np.array([0,0,0,1,0,1,1,1,0,0], dtype=np.bool_) # de Bruijn sequence\n",
    "\n",
    "    return rule(width=10, height=2, init=init)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "836c4d2b-4606-48d1-904c-3271fb06aa11",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFAAAAAQCAAAAACkIqcdAAAANUlEQVR4nGNkwAGeQWkpND46kELjM+EykFwwauBIMJARPX3hSnfo4ujpDyY++L08auAgNBAAfO8GBaMiIwcAAAAASUVORK5CYII=",
      "text/plain": [
       "<PIL.Image.Image image mode=L size=80x16>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "@automaton_rule\n",
    "def rule90_automaton(a,b,c):\n",
    "    \"Wolfram rule 90\"\n",
    "    if a == c:\n",
    "        return white\n",
    "    return black\n",
    "\n",
    "show(show_rule(rule90_automaton))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "181f23e1-d344-420b-948d-2a334678a75a",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<PIL.Image.Image image mode=L size=2048x1024>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show(rule90_automaton())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "551fc769-6a3c-41ee-a261-bce431a3a8f1",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<PIL.Image.Image image mode=L size=2048x1120>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# If width is a power of 2 then it cancels out after width/2 steps\n",
    "show(rule90_automaton(width=256, height=140, init=rand_init))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "46ffb177-ea74-4ba7-abca-3ad123f0836a",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def wolfram(n):\n",
    "    \"Generate rules by wolfram number\"\n",
    "    @automaton_rule\n",
    "    def rule(a,b,c):\n",
    "        return n & (1<<(~a*4+~b*2+~c)) == 0\n",
    "    return rule"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "2c0813dc-e94c-45ac-9743-3ac3cce2eaf2",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFAAAAAQCAAAAACkIqcdAAAANUlEQVR4nGNkwAGeQWkpND46kELjM+EykFwwauBIMJARPX3hSnfo4ujpDyY++L08auAgNBAAfO8GBaMiIwcAAAAASUVORK5CYII=",
      "text/plain": [
       "<PIL.Image.Image image mode=L size=80x16>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show(show_rule(wolfram(90)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "e89ab659-af48-429a-ae8c-e63a05a5bdee",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<PIL.Image.Image image mode=L size=2080x1040>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show(wolfram(90)(height=130, init=single_init))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "0787273f-c06f-4959-b33d-f4d53923d19b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<PIL.Image.Image image mode=L size=1016x480>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show(wolfram(90)(width=127,height=60, init=rand_init))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "6cdf7c79-03c8-4c8d-83e0-525340e6c74e",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFAAAAAQCAAAAACkIqcdAAAANElEQVR4nGNkwAGeQWkpND46kELjM+EykFwwauBIMJARPX2hpysYIKQOJj/4vTxq4CA0EAAWoQUFDWxgSQAAAABJRU5ErkJggg==",
      "text/plain": [
       "<PIL.Image.Image image mode=L size=80x16>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show(show_rule(wolfram(110)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "823b0a36-9dd9-409a-9a12-95cde6305124",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<PIL.Image.Image image mode=L size=4096x2048>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show(wolfram(110)(height=256))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "a7f5e142-00e3-4dca-924c-8ac7e18363e2",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<PIL.Image.Image image mode=L size=4096x2048>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show(wolfram(110)(height=256, init=rand_init))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "e163fc97-0442-4d2a-af20-de3e4a823722",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<PIL.Image.Image image mode=L size=4096x2048>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show(wolfram(45)(height=256))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a65954d7-b7c6-470c-8073-8c1a36479b47",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:symmart]",
   "language": "python",
   "name": "conda-env-symmart-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}