examples/tridimensional.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3D Cellular Automata\n",
    "Example for a three-dimensional Moore cellular automata with two possible states.\n",
    "Every cell interacts with its current state and the twenty six neighbours, which are the cells that are horizontally, vertically or\n",
    "diagonally adjacent. For this example, we use ndautomata as main library to generate the Automaton class, together with numpy for additional operations and matplotlib to generate some analytic images."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import ndautomata as ca\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from ndautomata import initializers, neighbours"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the abstract class `ndautomata.BaseAutomaton` we generate the 3DMoore `Automaton` class defining a regular array of 3 dimensions index. Radius is set to 1 to limit the number of neighbours to the 26 closest cells located on the three main dimension axes, diagonals additionally to the own cell state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Automaton(ca.BaseAutomaton):\n",
    "    neighbours = neighbours.regular(ndim=3, r=1)\n",
    "    states = 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this example, we will generate a Generic rule for our cellular automata evolution. To do so, as first step, it is required to generate a connections array space for a rule function with 27 arguments for each of the neighbours:\n",
    "\n",
    "$$a{_{i,j,k}^{t+1}} = \\phi \\begin{bmatrix} a{_{i-1,j-1,k-1}^{t}}, & ... & a{_{i+1,j+1,k+1}^{t}} \\end{bmatrix}$$\n",
    "\n",
    "As the space of possible rules is too large to represent as a string ($2^{134217728}$), we can generate a random base rule and set some of the properties. In this case we set every 3rd element in the rule combination to return '0' as next state. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "connections = [Automaton.states] * Automaton.neighbours.size\n",
    "rule = initializers.random(states=Automaton.states, size=connections)\n",
    "rule[1::3] = 0  # Constrain for the rule"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once the rule is set, an automata instance can be generated. To do so, we use again the `initializers` module to generate the initial conditions. In this example, we start with a a unique active state *1* located at the center of the initial conditions. All the rest of cells start with the value *0*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "ic = initializers.center(states=Automaton.states, size=[40, 40, 40])\n",
    "automaton = Automaton(ic, rule)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, with the help of `matplotlib` we can generate a plot with the cellular automaton information. For the aim os simplicity, we will generate 3 plots where each represents on the horizontal axis the average of states on a perpendicular spatial region of a main coordinate, and the vertical axis a time on the evolution process. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.rcParams[\"image.cmap\"] = \"binary\"\n",
    "data = np.array([next(automaton) for _ in range(40)])\n",
    "fig, axs = plt.subplots(1, automaton.dimensions)\n",
    "for dim in range(automaton.dimensions):\n",
    "    axis = tuple(d + 1 for d in range(automaton.dimensions) if d != dim)\n",
    "    axs[dim].matshow(np.mean(data, axis=axis))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Total runtime is around `0.8s` on a `Intel(R) Core(TM) i5-8365U CPU @ 1.60GHz`."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3.10.4 ('num')",
   "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": "3.10.4"
  },
  "orig_nbformat": 4,
  "vscode": {
   "interpreter": {
    "hash": "0ab3db896664fafbadca4c04ef00c5dfeb8d297cf9d1cdd228cc8c7cea1bef3f"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}