{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Autômatos Celulares"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Autômatos celulares são interessantes pois são modelos simples que podem apresentar comportamentos extremamente complexos, demonstrando o conceito importante em ciência da complexidade de que o comportamento de um sistema pode ser inesperado mesmo quando conhecemos detalhadamente o comportamento dos elementos que o compõe.\n",
    "\n",
    "Um autômato celular tem as seguintes características:\n",
    "\n",
    "- Ele se compõe de um conjunto discreto de $n$ **células**, geralmente denominadas por um índice $i=1,\\ldots,n$.\n",
    "- A operação dinâmica ocorre em instantes discretos de tempo $t\\in\\mathbb{N}$.\n",
    "- A cada célula $i$ em cada instante $t$ temos um estado $s_i(t)$. Muitas vezes, o conjunto de valores possíveis para o estado é discreto e mesmo finito.\n",
    "- Cada célula $i$ tem um conjunto de **células vizinhas** $N_i$. Muitas vezes o arranjo de células vizinhas é bastante regular considerando uma distribuição espacial das células.\n",
    "- O estado de todas as células é atualizado simultaneamente de $t$ para $t+1$.\n",
    "- O estado no instante $t+1$ de uma célula depende apeans do estado em $t$ da própria célula $s_i(t)$ e de suas vizinhas $s_j(t), j\\in N_i$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Autômatos celulares elementares"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vejamos o que talvez seja o caso mais simples de autômatos celulares.\n",
    "\n",
    "Neste caso, consideramos que as células estão distribuídas em um arranjo linear e cada célula $i$ tem como vizinhos as células $i-1$ (esquerda) e $i+1$ (direita).\n",
    "\n",
    "Neste arranjo, precisamos considerar os casos especiais das células $i=1$ e $i=n$, isto é, precisamos definir as condições de contorno. Usaremos aqui condições de contorno periódicas, isto é, consideramos que a célula à esquerda da célula 1 é a célula $n$ e a célula à direita da célula $n$ é a célula 1.\n",
    "\n",
    "O estado nestes autômatos é restrito ao conjunto $\\{0,1\\}$.\n",
    "\n",
    "Falta agora estabelecer as regras de atualização. Essas regras serão algo da forma:\n",
    "\n",
    "| esquerda | célula | direita | novo estado |\n",
    "|--------------|----------|--------------|------------|\n",
    "| 0 | 0 | 0 | 0 |\n",
    "| 0 | 0 | 1 | 0 |\n",
    "| 0 | 1 | 0 | 0 |\n",
    "| 0 | 1 | 1 | 1 |\n",
    "| 1 | 0 | 0 | 1 |\n",
    "| 1 | 0 | 1 | 1 |\n",
    "| 1 | 1 | 0 | 0 |\n",
    "| 1 | 1 | 1 | 1 |\n",
    "\n",
    "Esta tabela diz, por exemplo, que se para uma célula qualquer, se ela estiver em 1, a sua vizinha da esquerda estiver em 1 e a sua vizinha da direita estiver em 0, então ela passará a ter o valor 0 no próximo instante de tempo."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Numeração das regras"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Na tabela acima, o que distingue uma regra da outra são os valores na coluna *novo estado*. Como temos 8 linhas nessa coluna, e como cada linha pode ter 2 valores distintos, então vemos que o total de regras possíveis para esse tipo de autômato celular é $2^8=256$.\n",
    "\n",
    "Wolfram, que estudou esses autômatos detalhadamente, propôs uma numeração para identificá-los, que consiste em ler os números da coluna *novo estado* como um número binário, com a entrada correspondente à última linha sendo o bit mais significativo, e a entrada da primeira linha sendo o bit menos significativo. Assim, a regra da tabela acima é denominada **regra 184**, pois $1\\cdot2^7+0\\cdot2^6+1\\cdot2^5+1\\cdot2^4+1\\cdot2^3+0\\cdot2^2+0\\cdot2^1+0\\cdot2^0=184$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Condições iniciais"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para executar a dinâmica, falta especificar as condições iniciais $s_i(0)$.\n",
    "\n",
    "Com $n$ células, cada uma com 2 estados possíveis por célula, o número total de estados entre os quais escolher a condição inicial é $2^n$.\n",
    "\n",
    "Aqui vamos considerar apenas duas formas de inicialização:\n",
    "\n",
    "1. **Perturbação pontual:** Neste caso, uma das células é inicializada em $1$, enquanto todas as outras são inicializadas em $0$.\n",
    "2. **Aleatória:** Neste caso, o valor inicial de cada célula é escolhido aleatoriamente de modo que ela tem valor $1$ com probabilidade $p$ e valor $0$ com probabilidade $1-p$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Códigos"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos agora preparar alguns códigos para ajudar a estudar esses autômatos celulares.\n",
    "\n",
    "Representamos uma regra por uma lista que tem no índice $i$ a entrada da coluna de novo estado da $i$-ésima linha da tabela dessa regra. Para saber o novo valor do estado de uma célula, basta ler a entrada correspondente dados os valores da célula e seus vizinhos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def digits(n, b, m):\n",
    "    \"\"\"Computes the m least significative digits of n in base b.\"\"\"\n",
    "    alldigits = np.zeros(m, dtype=np.int)\n",
    "    i = 0\n",
    "    while i < m and n != 0:\n",
    "        alldigits[i] = n % b\n",
    "        n //= b\n",
    "        i += 1\n",
    "    return alldigits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Rule:\n",
    "    # Initializa an np.array of int with the rule table\n",
    "    def __init__(self, rule_code):\n",
    "        \"\"\"Creates a table for the rule given by rule_code\"\"\"\n",
    "        self.table = digits(rule_code, 2, 8)\n",
    "            \n",
    "    def next_state(self, s):\n",
    "        \"\"\"s is the current value of s[i-1], s[i], s[i+1]. Lookup table for next state.\"\"\"\n",
    "        return self.table[s[0]*4+s[1]*2+s[2]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Agora precisamos de uma função para plotar uma evolução temporal de um autômato celular."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_evolution(evolution, nstates=2):\n",
    "    \"\"\"Plots the time evolution of the states given in evolution.\n",
    "    Input should have one time step per line and one cell per column.\n",
    "    0 is ploted white; 1 is ploted black.\"\"\"\n",
    "    plt.matshow(evolution, vmin=0, vmax=nstates-1, cmap='binary')\n",
    "    plt.xticks([])\n",
    "    plt.yticks([])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Precisamos também funções para criar a condição inicial de um autômato, dado o tamanho do autômato e a probabilidade de estado 1, para o caso de inicialização aleatória."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def init_perturbation(n):\n",
    "    \"\"\"Inicializes an elementary cellular automaton with just one cell 1 in the centre.\"\"\"\n",
    "    res = np.zeros(n, dtype=np.int)\n",
    "    res[n//2] = 1\n",
    "    return res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def init_random(n, p):\n",
    "    \"\"\"Initializes an elementary cellular automaton with a probability p for each cell to be 1.\"\"\"\n",
    "    return (np.random.random(n) < p).astype(np.int)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A próxima função calcula a evolução de um autômato celular, dada a regra, uma condição inicial e o número de passos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def evolve(rule, init, T):\n",
    "    \"\"\"Evolves the elementary automaton given by rule from the initial condition init for T time steps.\"\"\"\n",
    "    n = init.size\n",
    "    evolution = np.zeros((T+1, n), dtype=np.int)\n",
    "    evolution[0, :] = init\n",
    "    for t in range(T):\n",
    "        evolution[t+1, 0] = rule.next_state([evolution[t, n-1], evolution[t, 0], evolution[t, 1]])\n",
    "        for i in range(1, n-1):\n",
    "            evolution[t+1, i] = rule.next_state(evolution[t, (i-1):(i+2)])\n",
    "        evolution[t+1, n-1] = rule.next_state([evolution[t, n-2], evolution[t, n-1], evolution[t, 0]])\n",
    "    return evolution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dualidade"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Entre as 256 regras possíveis, existe uma relação duas a duas, que chamaremos de **dualidade**.\n",
    "\n",
    "Seja uma regra $r$ com código $$r=\\sum_{j=0}^{7}r_i 2^i,$$ onde $r_i$ são os dígitos binários do seu código. Consideremos agora a regra $$\\bar{r}=\\sum_{j=0}^{7}\\bar{r}_{8-j}2^j,$$ onde $\\bar{r}_i$ é o inverso do dígito binário $r_i$, isto é,\n",
    "$$\\bar{r}_i = 1 - r_i.$$\n",
    "\n",
    "Denominamos a regra $\\bar{r}$ como a regra **dual** de $r$. A procedimento acima indica que para achar a regra dual pegamos a representação binária com 8 bits, invertemos cada um dos bits e depois revertemos a ordem dos bits.\n",
    "\n",
    "Por exemplo, Para a regra 184, que tem representação binária 10111000 invertemos para 00011101 e então trocamos os bits para 11100010, isto é, a dual da regra 184 é a regra 226.\n",
    "\n",
    "Algumas regras são duas de si mesmas. Por exemplo a regra 23: 00010111 inverte para 11101000 e trocamos os bits para 00010111, isto é, 23.\n",
    "\n",
    "Note que a dualidade é recíproca: Se $r_2$ é dual de $r_1$, então $r_1$ é dual de $r_2$.\n",
    "\n",
    "Também podemos definir uma dualidade para estados: Dado um estado $$s = (s_1, s_2, \\ldots, s_n),$$ o seu dual é $$\\bar{s} = (\\bar{s}_1, \\bar{s}_2, \\ldots, \\bar{s}_n).$$\n",
    "\n",
    "A seguinte propriedade pode ser verificada com facilidade:\n",
    "\n",
    "---\n",
    "Se a evolução temporal de uma regra $r$ partindo de um estado inicial $s(0)$, é $s(t)$, então a evolução da regra dual $\\bar{r}$ partindo do estado dual $\\bar{s}(0)$ será dual: $\\bar{s}(t)$.\n",
    "\n",
    "---\n",
    "\n",
    "Para ver isso, vamos criar alguns códigos e verificar alguns exemplos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dual_state(state):\n",
    "    return 1 - state\n",
    "\n",
    "def dual_rule(rule):\n",
    "    newrule = Rule(0)\n",
    "    newrule.table = 1 - np.flip(rule.table)\n",
    "    return newrule"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "T = 20\n",
    "s0 = init_perturbation(2 * T + 1)\n",
    "s0_bar = dual_state(s0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 562.286x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(6), s0, T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 562.286x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(dual_rule(Rule(6)), dual_state(s0), T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 562.286x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(50), s0, T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 562.286x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(dual_rule(Rule(50)), dual_state(s0), T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 562.286x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(220), s0, T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 562.286x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(dual_rule(Rule(220)), dual_state(s0), T))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vejamos um caso de regra que é dual dela mesma:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 562.286x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(23), s0, T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 562.286x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(dual_rule(Rule(23)), dual_state(s0), T))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mas não se confunda: a evolução é dual quando se começa de condições iniciais duais. Se se começa da mesma condição inicial, a evolução pode ser não relacionada."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 562.286x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(6), s0, T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 562.286x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(dual_rule(Rule(6)), s0, T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 562.286x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(50), s0, T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAcUAAAD0CAYAAADqkD04AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAFNklEQVR4nO3cQU4rRxRAUTv6SyDjeA+w/xXAHsg47KH/5I4CUboEjanqc6a2nrpL8r8qpP+u27ZdAIDL5Y97PwAA/BSiCAARRQCIKAJARBEAIooAEFEEgIgiAEQUASC/Rr788PCw3W63gx4Fzufl5WXX9x4fHw9+EjiP19fXy9vb2/Wjz4aieLvdLs/Pz1/zVMDlev3wd/mO3x18naenp//8zJ9PASCiCAARRQCIKAJARBEAIooAEFEEgIgiAOS6bdv+L1+v+78M/K+9v7+9/8kf2Gfbtg9/VG6KABBRBICIIgBEFAEgoggAEUUAiCgCQEQRACKKAJBf934AWM3glqi7zQTec1MEgIgiAEQUASCiCAARRQCIKAJARBEAIooAEFEEgIgiAMSaN9jhqDVre+ceMXN0LpyBmyIARBQBIKIIABFFAIgoAkBEEQAiigAQUQSAiCIARBQBINa8cWqzrFmbac0czMxNEQAiigAQUQSAiCIARBQBIKIIABFFAIgoAkBEEQBiow3LOftGmZneH34aN0UAiCgCQEQRACKKABBRBICIIgBEFAEgoggAEUUAiCgCQKx5Yxr3XIm26pq1Wc4UvoubIgBEFAEgoggAEUUAiCgCQEQRACKKABBRBICIIgBEFAEg1rxxV7OsRFtxzdrI3Flmwme5KQJARBEAIooAEFEEgIgiAEQUASCiCAARRQCIKAJAbLThy624/WXFjTIjc2eZOToX/s1NEQAiigAQUQSAiCIARBQBIKIIABFFAIgoAkBEEQAiigAQa97YbZb1XbPMHJnrTO97ppyHmyIARBQBIKIIABFFAIgoAkBEEQAiigAQUQSAiCIARBQBINa8ndzZ13edec3ayNxZZo7MPepMmZubIgBEFAEgoggAEUUAiCgCQEQRACKKABBRBICIIgDERpsFrbj9ZGTuLDNH5jrT9c6Un8lNEQAiigAQUQSAiCIARBQBIKIIABFFAIgoAkBEEQAiigAQa94mMsv6qhXXdznTOWaOzJ3pTPk+booAEFEEgIgiAEQUASCiCAARRQCIKAJARBEAIooAEFEEgFjzdmdnX181y/s70zlmjsxd8Uz5PDdFAIgoAkBEEQAiigAQUQSAiCIARBQBIKIIABFFAIiNNgewqWO993emc8wcmbvimY7O5T03RQCIKAJARBEAIooAEFEEgIgiAEQUASCiCAARRQCIKAJArHkbMMv6prOvr5pl5shcZ+pM9zri/c/ETREAIooAEFEEgIgiAEQUASCiCAARRQCIKAJARBEAIooAkNOveTv7+ibv70xXmjkyd8UzHZl71PvPzk0RACKKABBRBICIIgBEFAEgoggAEUUAiCgCQEQRALLsRhubOr525sjcFd/fmc4xc2Tuimc6MvfeM38qN0UAiCgCQEQRACKKABBRBICIIgBEFAEgoggAEUUAiCgCQKZa8zbLqqUV1zeNzF3x/Z3pHDNH5q54piNzZ5n53dwUASCiCAARRQCIKAJARBEAIooAEFEEgIgiAEQUASCiCAC5+5q3FVctrbi+aWTuiu/vTOeYOTJ3xTMdmTvLzNG5n+WmCAARRQCIKAJARBEAIooAEFEEgIgiAEQUASCiCAA5bKPNLBsQZpk5MnfFMx2ZO8vMkbnO1Jnu5d++z3FTBICIIgBEFAEgoggAEUUAiCgCQEQRACKKABBRBICIIgDkOriW55/L5fL3cY8DAIf7a9u2Pz/6YCiKALAyfz4FgIgiAEQUASCiCAARRQCIKAJARBEAIooAEFEEgPwGtMic6AqZqnEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 562.286x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(dual_rule(Rule(50)), s0, T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 562.286x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(220), s0, T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 562.286x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(dual_rule(Rule(220)), s0, T))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reversão binária"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Outra relação existente entre as regras é a reversão binária. Neste caso, para uma combinação de estados da célula e de suas vizinhas em que uma das regras produz 0, a outra produz 1, e vice-versa.\n",
    "\n",
    "Esta relação corresponde à inversão binária do número de regra, isto é, dada uma regra $r=\\sum_{i=0},^7r_i 2^i$, a sua reversa será a regra $$\\sum_{i=0}^7(1-r_i)2^i=\\sum_{i=0}^7 2^i - \\sum_{i=0}^7r_i 2^i = 2^8 - 1 - r = 255 - r.$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 562.286x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(96), s0, T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 562.286x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(255-96), s0, T))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simetria direita-esquerda"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Outra relação entre regras é a simetria direita-esquerda, que ocorre quando uma regra é similar à outra se trocarmos as prescrições de \"direita\" e \"esquerda\" na regra.\n",
    "\n",
    "Por exemplo, a regra 6 tem tabela\n",
    "\n",
    "| esquerda | célula | direita | novo estado |\n",
    "|--------------|----------|--------------|------------|\n",
    "| 0 | 0 | 0 | 0 |\n",
    "| 0 | 0 | 1 | 1 |\n",
    "| 0 | 1 | 0 | 1 |\n",
    "| 0 | 1 | 1 | 0 |\n",
    "| 1 | 0 | 0 | 0 |\n",
    "| 1 | 0 | 1 | 0 |\n",
    "| 1 | 1 | 0 | 0 |\n",
    "| 1 | 1 | 1 | 0 |\n",
    "\n",
    "Nesta regra 6, o novo estado é ligado apenas se a célula da **esquerda** está desligada e a da **direita** tem valor oposto. Revertendo \"direita\" e \"esquerda\" ficamos com a regra: _ligar o novo estado se a célula da **direita** estiver desligada e a da **esquerda** tiver valor oposto_, o que corresponde à tabela\n",
    "\n",
    "| esquerda | célula | direita | novo estado |\n",
    "|--------------|----------|--------------|------------|\n",
    "| 0 | 0 | 0 | 0 |\n",
    "| 0 | 0 | 1 | 0 |\n",
    "| 0 | 1 | 0 | 1 |\n",
    "| 0 | 1 | 1 | 0 |\n",
    "| 1 | 0 | 0 | 1 |\n",
    "| 1 | 0 | 1 | 0 |\n",
    "| 1 | 1 | 0 | 0 |\n",
    "| 1 | 1 | 1 | 0 |\n",
    "\n",
    "e portanto à regra de número 20.\n",
    "\n",
    "Dada uma regra com número $\\sum_{i=0}^{7}r_i 2^i$ ($r_i$ são os dígitos binários da regra), a sua simétrica será a regra de número $\\hat{r} = \\sum_{i=0}^{7}\\hat{r}_i 2^i$ onde $\\hat{r}_1=r_4, \\hat{r}_4=r_1, \\hat{r}_3=r_6, \\hat{r}_6=r_3$ e $\\hat{r}_i = r_i$ para $i\\notin\\{1, 4, 3, 6\\}$. A diferença numérica entre duas regras simétricas é então\n",
    "$$(r_6-r_3)(2^6-2^3) + (r_4-r_1)(2^4-2^1) = 56(r_6-r_3) + 14(r_4-r_1).$$\n",
    "\n",
    "Vemos que, caso $r_1=r_4$ e $r_3=r_6$ então a regra é simétrica dela mesma, e portanto tem comportamento simétrico direita-esquerda."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def symmetric_rule(r):\n",
    "    newrule = r\n",
    "    newrule.table[1], newrule.table[4] = r.table[4], r.table[1]\n",
    "    newrule.table[3], newrule.table[6] = r.table[6], r.table[3]\n",
    "    return newrule"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAcUAAAD0CAYAAADqkD04AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAEcklEQVR4nO3cvW1jVxRG0UfDJSg3e5D6r0DsQc7Vw3HgDSczg3lX0DP/1krJ4CbCxiGg7zQzGwCwbX9c+wEAcCtEEQAiigAQUQSAiCIARBQBIKIIABFFAIgoAkD+XPnyy8vLnM/ng54Cz+dyuez63uvr68Evgefx8fGxfX5+nn722VIUz+fz9v7+/j2vArbT6ad/lz/wdwff5+3t7Zef+fkUACKKABBRBICIIgBEFAEgoggAEUUAiCgCQJb+eR/4vb3/kA/cHpciAEQUASCiCAARRQCIKAJARBEAIooAEFEEgIgiAMSiDeywslIzMwe+BDiSSxEAIooAEFEEgIgiAEQUASCiCAARRQCIKAJARBEAIooAEDNvPLWV+Tbg8bkUASCiCAARRQCIKAJARBEAIooAEFEEgIgiAEQUASCiCAAx88bDWZlum5kDXwLcG5ciAEQUASCiCAARRQCIKAJARBEAIooAEFEEgIgiAMSiDXdjZakG4CtcigAQUQSAiCIARBQBIKIIABFFAIgoAkBEEQAiigAQUQSAmHnjqlam22bmwJcAuBQB4D+iCAARRQCIKAJARBEAIooAEFEEgIgiAEQUASCiCAAx88a3W5luA7glLkUAiCgCQEQRACKKABBRBICIIgBEFAEgoggAEUUAiEUbdtu7VDMzB78E4BguRQCIKAJARBEAIooAEFEEgIgiAEQUASCiCAARRQCIKAJAzLw9ub3TbQDPwKUIABFFAIgoAkBEEQAiigAQUQSAiCIARBQBIKIIABFFAIiZtwe0Mt02Mwe+BOC+uBQBIKIIABFFAIgoAkBEEQAiigAQUQSAiCIARBQBIBZt7sjKUg0A61yKABBRBICIIgBEFAEgoggAEUUAiCgCQEQRACKKABBRBICYebuylem2mTnwJQC4FAEgoggAEUUAiCgCQEQRACKKABBRBICIIgBEFAEgoggAMfN2gJXpNgBuh0sRACKKABBRBICIIgBEFAEgoggAEUUAiCgCQEQRAGLRZsHepZqZOfglABzBpQgAEUUAiCgCQEQRACKKABBRBICIIgBEFAEgoggAEUUAyNPPvO2dbgPg8bkUASCiCAARRQCIKAJARBEAIooAEFEEgIgiAEQUASCiCAB52Jm3vfNtM3PwSwC4Fy5FAIgoAkBEEQAiigAQUQSAiCIARBQBIKIIABFFAMhdLdrsXakBgK9wKQJARBEAIooAEFEEgIgiAEQUASCiCAARRQCIKAJARBEAcvWZt5Xptpk58CUAPDuXIgBEFAEgoggAEUUAiCgCQEQRACKKABBRBICIIgBEFAEgh828rcy3AcAtcCkCQEQRACKKABBRBICIIgBEFAEgoggAEUUAiCgCQJYWbS6Xy+6lmpn50oMA4FpcigAQUQSAiCIARBQBIKIIABFFAIgoAkBEEQAiigAQUQSALM28bdv2uW3b33u+uHcODgD+Z3/96oOTjVIA+JefTwEgoggAEUUAiCgCQEQRACKKABBRBICIIgBEFAEg/wDk/TpK1Ex2DgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 562.286x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(6), s0, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 562.286x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(symmetric_rule(Rule(6)), s0, T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAcUAAAD0CAYAAADqkD04AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAEaElEQVR4nO3cvW3bUBiG0csgIzh1tIO9/wT2Dk4d78A0TxfFuQr0w5DntFTBRnjwCdC7rOs6AIAxvjz6BQBgK0QRACKKABBRBICIIgBEFAEgoggAEUUAiCgCQL5e8uGnp6f1dDrd6FXgeN7e3qY+9/z8fOM3geN4f38fHx8fy7lnF0XxdDqN19fX67wVMJbl7PfyN753cD0vLy9/fObnUwCIKAJARBEAIooAEFEEgIgiAEQUASCiCAC56M/7wGPM/sl/jDHWdb3hm8C+uRQBIKIIABFFAIgoAkBEEQAiigAQUQSAiCIARBQBIBZtYGes38C/cykCQEQRACKKABBRBICIIgBEFAEgoggAEUUAiCgCQEQRAGLmDQ5sdhLOHBxH4VIEgIgiAEQUASCiCAARRQCIKAJARBEAIooAEFEEgIgiAMTMG/BXs3NwY5iE4//mUgSAiCIARBQBIKIIABFFAIgoAkBEEQAiigAQUQSAWLQBrmp2/cbyDVvkUgSAiCIARBQBIKIIABFFAIgoAkBEEQAiigAQUQSAiCIAxMwb8BCzc3BjmITjflyKABBRBICIIgBEFAEgoggAEUUAiCgCQEQRACKKABBRBICYeQM2zyQc9+JSBICIIgBEFAEgoggAEUUAiCgCQEQRACKKABBRBIBYtAF2ZXb9xvIN57gUASCiCAARRQCIKAJARBEAIooAEFEEgIgiAEQUASCiCAAx8wYc0uwc3Bgm4Y7EpQgAEUUAiCgCQEQRACKKABBRBICIIgBEFAEgoggAEUUAiJk3gL8wCXccLkUAiCgCQEQRACKKABBRBICIIgBEFAEgoggAEUUAiEUbgCuaXb+xfLNNLkUAiCgCQEQRACKKABBRBICIIgBEFAEgoggAEUUAiCgCQMy8ATzA7BzcGCbh7smlCAARRQCIKAJARBEAIooAEFEEgIgiAEQUASCiCAARRQCImTeAjTMJdz8uRQCIKAJARBEAIooAEFEEgIgiAEQUASCiCAARRQCIRRuAHZldv7F8c55LEQAiigAQUQSAiCIARBQBIKIIABFFAIgoAkBEEQAiigAQM28ABzQ7BzfGsSbhXIoAEFEEgIgiAEQUASCiCAARRQCIKAJARBEAIooAEFEEgJh5A+BTs5Nwe5iDcykCQEQRACKKABBRBICIIgBEFAEgoggAEUUAiCgCQCzaAHAVs8s3Y2x3/calCAARRQCIKAJARBEAIooAEFEEgIgiAEQUASCiCAARRQCImTcA7m6rk3AuRQCIKAJARBEAIooAEFEEgIgiAEQUASCiCAARRQCIKAJAzLwBsGmzk3DXmINzKQJARBEAIooAEFEEgIgiAEQUASCiCAARRQCIKAJALNoAsAuzyzefcSkCQEQRACKKABBRBICIIgBEFAEgoggAEUUAiCgCQEQRALKs6zr/4WX5Ocb4cbvXAYCb+76u67dzDy6KIgDsmZ9PASCiCAARRQCIKAJARBEAIooAEFEEgIgiAEQUASC/AKQhWNMJXeqiAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 562.286x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(220), s0, T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAcUAAAD0CAYAAADqkD04AAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAEMklEQVR4nO3csa3aABhGURNlBPqwA+w/Ad6B9Ozg19wokfJQ8BMOYJ/TmsINuvqR+HbTNA0AwDB8e/YLAMCrEEUAiCgCQEQRACKKABBRBICIIgBEFAEgoggA+T7nw/v9fjocDgu9CmzPOI53fe54PC78JrAdl8tluF6vu8+ezYri4XAYzufzY94KGHa7T7+Xf/G9g8c5nU43n/n5FAAiigAQUQSAiCIARBQBIKIIABFFAIgoAkBm/Xkf+Ld7/5APvB6XIgBEFAEgoggAEUUAiCgCQEQRACKKABBRBICIIgDEog3cwUoNbINLEQAiigAQUQSAiCIARBQBIKIIABFFAIgoAkBEEQAiigAQM29smvk24E8uRQCIKAJARBEAIooAEFEEgIgiAEQUASCiCAARRQCIKAJAzLyxOqbbgK9yKQJARBEAIooAEFEEgIgiAEQUASCiCAARRQCIKAJALNrwNizVAEtzKQJARBEAIooAEFEEgIgiAEQUASCiCAARRQCIKAJARBEAYuaNpzLdBrwSlyIARBQBIKIIABFFAIgoAkBEEQAiigAQUQSAiCIARBQBIGbeeDjTbcC7cikCQEQRACKKABBRBICIIgBEFAEgoggAEUUAiCgCQCzacDdLNcDauRQBIKIIABFFAIgoAkBEEQAiigAQUQSAiCIARBQBIKIIADHztnGm2wB+cykCQEQRACKKABBRBICIIgBEFAEgoggAEUUAiCgCQEQRAGLmbYVMtwF8jUsRACKKABBRBICIIgBEFAEgoggAEUUAiCgCQEQRAGLR5o1YqgFYlksRACKKABBRBICIIgBEFAEgoggAEUUAiCgCQEQRACKKABAzb09mug3gdbgUASCiCAARRQCIKAJARBEAIooAEFEEgIgiAEQUASCiCAAx87YA020A78mlCAARRQCIKAJARBEAIooAEFEEgIgiAEQUASCiCACxaDODpRqAdXMpAkBEEQAiigAQUQSAiCIARBQBIKIIABFFAIgoAkBEEQCy+Zk3020A/OJSBICIIgBEFAEgoggAEUUAiCgCQEQRACKKABBRBICIIgBktTNv5tsAmMulCAARRQCIKAJARBEAIooAEFEEgIgiAEQUASCiCAB5q0UbKzUALMmlCAARRQCIKAJARBEAIooAEFEEgIgiAEQUASCiCAARRQDI02feTLcB8CpcigAQUQSAiCIARBQBIKIIABFFAIgoAkBEEQAiigAQUQSALDbzZr4NgHfjUgSAiCIARBQBIKIIABFFAIgoAkBEEQAiigAQUQSAzFq0GcfRUg0Aq+VSBICIIgBEFAEgoggAEUUAiCgCQEQRACKKABBRBICIIgBk1szbMAzXYRh+LvEiwG3mFeGhftx6sJum6X++CAC8LD+fAkBEEQAiigAQUQSAiCIARBQBIKIIABFFAIgoAkA+AD7bHGjp2+GNAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 562.286x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(symmetric_rule(Rule(220)), s0, T))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Alguns estudos de caso simples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vejamos agora que tipos de comportamento encontramos em autômatos celulares, executando algumas regras para uma perturbação e para estados aleatórios com probabilidade de 0.1, 0.3, e 0.5 do estado de uma célular ser 1.\n",
    "\n",
    "Note que a regra 0 é desinteressante, pois o próximo estado é sempre 0, não importa o estado atual. Da mesma forma, a regra dual 255 tem o próximo estado sempre 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "T = 100\n",
    "s0_pert = init_perturbation(2 * T + 1)\n",
    "s0_p1 = init_random(100, 0.1)\n",
    "s0_p3 = init_random(100, 0.3)\n",
    "s0_p5 = init_random(100, 0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regras 204, 240 e 170"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos começar com a regra 204."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "r = Rule(204)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 573.149x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(r, s0_pert, T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPEAAAD2CAYAAAAHzmGxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAADbklEQVR4nO3aQWobMRiAUU3pEdx1fQfP/U8wvoOzju+gLEIgCxdiGuP5wnvbEUL8wwdaaJlzDqDr17MPAPwfEUOciCFOxBAnYogTMcSJGOJEDHEihrjf9yw+HA7zeDyO8/k8xhjjdDo95FA/zce8xnjOzPbwv75rBnub5SNn+3nvy+Uyrtfrcmvdcs+zy3Vd57ZtY1ne9/Jk82s+5jXGc2a2h//1XTPY2ywfOdvPe6/rOrZtuxmx6zTEiRjiRAxxIoY4EUOciCFOxBAnYogTMcSJGOJEDHEihjgRQ5yIIU7EECdiiBMxxIkY4kQMcSKGOBFDnIghTsQQJ2KIEzHEiRjiRAxxIoY4EUOciCFOxBAnYogTMcSJGOJEDHEihjgRQ5yIIU7EECdiiBMxxIkY4kQMcSKGOBFDnIghTsQQJ2KIEzHEiRjiRAxxIoY4EUOciCFOxBAnYogTMcSJGOJEDHEihjgRQ5yIIU7EECdiiBMxxIkY4kQMcSKGOBFDnIghTsQQJ2KIEzHEiRjiRAxxIoY4EUOciCFOxBAnYogTMcSJGOJEDHEihjgRQ5yIIU7EECdiiBMxxIkY4kQMcSKGOBFDnIghTsQQJ2KIEzHEiRjiRAxxIoY4EUOciCFOxBAnYogTMcSJGOJEDHEihjgRQ5yIIU7EECdiiBMxxIkY4kQMcSKGOBFDnIghTsQQJ2KIEzHEiRjiRAxxIoY4EUOciCFOxBAnYogTMcSJGOJEDHEihjgRQ5yIIU7EECdiiBMxxIkY4kQMcSKGOBFDnIghTsQQJ2KIEzHEiRjiRAxxIoY4EUOciCFOxBAnYogTMcSJGOJEDHEihjgRQ5yIIU7EECdiiBMxxIkY4kQMcSKGOBFDnIghTsQQJ2KIEzHEiRjiRAxxIoY4EUOciCFOxBAnYogTMcSJGOJEDHEihjgRQ5yIIU7EECdiiBMxxIkY4kQMcSKGOBFDnIghTsQQJ2KIEzHEiRjiRAxxIoY4EUOciCFOxBAnYogTMcSJGOJEDHEihjgRQ5yIIU7EECdiiBMxxIkY4kQMcSKGOBFDnIghTsQQJ2KIEzHEiRjiRAxxIoY4EUOciCFOxBC3zDm/vnhZXscYL487DvAPf+ecf259uCtiYH9cpyFOxBAnYogTMcSJGOJEDHEihjgRQ5yIIe4NsBFQ364ywt4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 288x290.88 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(r, s0_p1, T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x290.88 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(r, s0_p3, T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x290.88 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(r, s0_p5, T))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vemos que a regra 204 sempre copia o estado inicial. Isso é fácil de entender le olharmos a sua tabela de evolução (204 em binário é 11001100):\n",
    "\n",
    "| esquerda | célula | direita | novo estado |\n",
    "|--------------|----------|--------------|------------|\n",
    "| 0 | 0 | 0 | 0 |\n",
    "| 0 | 0 | 1 | 0 |\n",
    "| 0 | 1 | 0 | 1 |\n",
    "| 0 | 1 | 1 | 1 |\n",
    "| 1 | 0 | 0 | 0 |\n",
    "| 1 | 0 | 1 | 0 |\n",
    "| 1 | 1 | 0 | 1 |\n",
    "| 1 | 1 | 1 | 1 |\n",
    "\n",
    "Note que o novo estado é sempre igual ao estado atual da célula, independente dos valores das células vizinhas.\n",
    "\n",
    "Algo similar ocorre com as regras que copiam o estado da célula da esquerda ou da célula da direita:\n",
    "\n",
    "| esquerda | célula | direita | novo estado |\n",
    "|--------------|----------|--------------|------------|\n",
    "| 0 | 0 | 0 | 0 |\n",
    "| 0 | 0 | 1 | 0 |\n",
    "| 0 | 1 | 0 | 0 |\n",
    "| 0 | 1 | 1 | 0 |\n",
    "| 1 | 0 | 0 | 1 |\n",
    "| 1 | 0 | 1 | 1 |\n",
    "| 1 | 1 | 0 | 1 |\n",
    "| 1 | 1 | 1 | 1 |\n",
    "\n",
    "Esta tabela corresponde à regra 240.\n",
    "\n",
    "| esquerda | célula | direita | novo estado |\n",
    "|--------------|----------|--------------|------------|\n",
    "| 0 | 0 | 0 | 0 |\n",
    "| 0 | 0 | 1 | 1 |\n",
    "| 0 | 1 | 0 | 0 |\n",
    "| 0 | 1 | 1 | 1 |\n",
    "| 1 | 0 | 0 | 0 |\n",
    "| 1 | 0 | 1 | 1 |\n",
    "| 1 | 1 | 0 | 0 |\n",
    "| 1 | 1 | 1 | 1 |\n",
    "\n",
    "Esta tabela corresponde à regra 170.\n",
    "\n",
    "Nestes casos, ocorre também uma \"cópia\", mas ela é deslocada no espaço à esquerda ou à direita."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "r = Rule(240)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 573.149x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(r, s0_pert, T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x290.88 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(r, s0_p1, T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 288x290.88 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(r, s0_p3, T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPEAAAD2CAYAAAAHzmGxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAXYUlEQVR4nO2dTbLrOK6E7Y5eQr1x1x6u978C1yJ6/BahnrQqVCwgmQmSx6Y6v4g7uBbxQ1ASSJD2eR7H8TDG7Ms/Pu2AMWYMP8TGbI4fYmM2xw+xMZvjh9iYzfFDbMzm+CE2ZnP8EBuzOX6IjdmcfyqNf/vtt+P3339//PHHH4/H4/H49evXn9eiz66fX6+1ba9t2rYRUfuejKKHIfId9b2nB8mhNkwMM33I98wX1Bb5h3TO8gfFZNbYtPLM2DA2mTgdx/GMZJ/Kscvn83n8V9n5/6uBv3wW6W2vRW2vOjM9WVtWTtHTI/K9tc3oR/Fi2kRj0sohfWjcFH96/rH6RvxB99WssWH8VPqObF30hEKeThuzOdJ0+oR500Vtsmsoo6O3Gco+zJuc0dODmY2gmQbSk8UCtYlsZfFWZ1LK2GQyav9G/Fk5NpX+oWcB2TqO4/F6vULfHg9nYmO2xw+xMZsjPcS/fv362/Tj/Hccx+M4jvT/7TQhaht9FtlqadteyWQikB6GrO+qjSxeTJtoTDL/VN8zf9DYtDKR7lX+oPtq1tgo/UPPgmKrxZnYmM0pFbaiRbmyfZQt/JE8stXKtu2RDNs/BabAwthgijBMG6YgpRSH2v8zY4PklP4p/qj31cjYVPvH2Ozdh87ExmzO0GGP5tpf/q9k2UgPk9FbvYnP6TWx73RbZCfrO6NfiXvUBr3ts2uM76o/Pf9YfT1/mH6uHBvGT7HvPuxhzB0pZeKT0TdnJSNnn2V6Mr9YOUUPg9J3Rg+SydpUMjLre+aPkpGR77P9qc4UEczMoDc2yTVnYmPuiB9iYzantMV0wpTnZ5X5la2Ttn1mK9OHWLX9dLU9sv2EtnuYmCpbe8o2Cxqb6PNK/yr+qMu9ke0ntX/Xaz47bcyNGTp2eeX5rB+lO/9//azVc36O5JE/rb6sgMBm2EwHS9aXXgx7Pkf9U2Ka+YeuRb6jPjBx7t0PjD9IbyuL7qtZY6P2j70fnYmN2Zxpxy5Psrn+9ZqyfYT0VNZ4TD8qa+RIDwOzNquuw3rrwGqdQVlXtrI9+RZlfcrcV5kskl8xNpX+ZTgTG7M5y45dnjBt1Szba5t9lunp9aEnp+hhUPrO6Mlk1Jhm/qm+K/4gGaV/I/4wM0WkJwLVlqI2r9fr8X6/fdjDmDvih9iYzSltMUWl7962DSrPj5b5o+2Q3tYJux3SyjGs2n5SbShxb9soW0yq74o/mQzanon0jfiD7qtZY8P0L8OZ2JjNmbbFxJTcmfL8rDJ/Jo9sof71ZCLYLYIMpnBX2eJgYsHEFI3N7O2eiGyMq/dVr59IftbYID8ynImN2ZzpW0y9sv8VZfupWuZnMjryJ2vLyCh6GJgtk+r2xurtp1nbPQhl24eZIWSykfzKsXk8vMVkzK2ZXp3OKoaoch3padtUK4Soyp3Ziuj14Scq10y1FcW71YP8UmIa6V5VKUYoFWN0X2V6kfzssVFmbM7ExmyOH2JjNmf5FtN16pAVPRg9s8r8qACBtk56fejJKXoYmMJdz0Y17kxM0djM3u7pyaj9q/jD3FfK2PT8uOJMbMzmDP3GFnr7KG/DK4weZfuI8aeXkVvdah8QqzLy9bPKW5+JOxPTarZm4t2Ls3o/zJ4hzB6bDGdiYzZn2mGPS5tH1ia7ht40SE/bRl3f9N682XZDBtouUahm5dZWJd6RnkxOiWkkh/QxsxnGn55/jD5mHc70c3RsDv94vDH3ZPqfcbm0Tdsob0NkS3mTj2Tkni22Dz05RQ9Dr+/fmpEZ31V/ev6x+kb8qc4ULzLOxMbcET/ExmzO0HT6CrPgz6ZzyrQa6YnaKNsYTNs7TqtZG0rc2zbM0uST02rk+wp/iss9T6eNuSNDhz2uZG+SnQ+EMG/OnQ+EXG3f8UAIszW0y4EQ/0E1Y27MtD+odvJ8zv0jUufnjK2rnrZNqz/6LPMzahv5lfU98ouJl6KHAcWitcHoQX4xY5zJoGvoXkF9YOLM3J+ZP1EsGX+ymKD+tTgTG7M50/+g2omyVkBrs3Z9Etll9CjrXGSTWTcrfY/6tHqdXKkPsHqYuDPrQaUGodRjmFqEcn8ysVT8Qf3LcCY2ZnOW/0G1K2htm7VBb05kM9MTtVEqjpU3J4qx0gdEJSNHtqrxbvUgGWaMsxgq4xihjE0kM3Jfqf5c5f1rl8bcGD/ExmyONJ1+vV7H+/2ePuWK5NG0hZnSKG2ZQosyBWSmfi2eVutLk96UW13GKFPr1dPqRN7TaWPuyFBhq5odM5lInikuMTaZjMJsHynZo5KRs/Y9GUUPw8oxZopLSgyZIpgyAxrJyKv8cWHLmBszbU1cyY4nszMysjv65qxsPzHruIhvWCevHOOfysjId9Wfnn+svqI/zsTG3JHpa+JVletPHAhhKs8+EKLb8IGQmj/OxMbcFD/ExmxO6VtMykGHaxs03UG6e7bQtBXZ7OlRt48yPUyc0HRM6QOCiT9i1RhHMsoYtzFk9KG4KWMTfV7pX88f/7KHMTdm6Jc9ns/+L19c25yc1xCtzJVWd/s5usbYitr2+olsMnFi+n61pcQr01Nl1RhH/WPGOJNB+pDvqA9MnJn7s+JPhjOxMZsz7Zc9mDk+s1ZoUdYuaG3W2ozsMm2V7SOkh4mT0veoT71MiGLBsHKMe+vdqI1S02B8b2V78i3K/an40+JMbMzmTP8j47MyVYtavc0yAVNJnfXmrGQP1lavDz05RU+PlWPMZFcmppVszcS7kpHV/vXGxJnYmM3xQ2zM5kz7obxLm7/8X51uZnoiGD+iLYJMHtlk2ipTZeQnks/0VPqAqEyrI1uzx5iJBYpp5p/qu+IPkmP75+8TG3Njpv/G1p+KJ2cqRCUjo2urMjJrk4lT5k/Pt54Mq4Nl5RijWV9mk5kpKr5nsqhtJEf2z5nYmDuy7De2LjJ/+2w0U2V8MiNH7ZVtNuSPssaLmJGRkR6GlWPMxEKZ1Sh1nQhlbBi9l2vOxMbckWVfRTzZ+UAIsnmHAyHMTIrRw/CJAyFqTL/5QIi/imjMjfFDbMzmLPs+ccTZppU/P7/KI32tnojMj8hWe02xeY1Br59Rv9r/I39QnJA/TNzQuCl6GFaNMRMLFNPMP9V3xZ9Mpqf7ijOxMZvzo98nzuSZwgFT0IhQ/EB6GZuMHmX7iPFHKdRksqgPiJFCV2Rr1hgzsagWC5XibKY3093CxteZ2JjNmfYFiGhN036O1mMtSqZCejK9yA/UP8XmaJwUf1CckD9ZW0ZG0cOwcoyZWKDs2sohfUyWVcbm8Xj4CxDG3JlSdZqpJqKKagtTIUQVXqSnhaneov4pNkfjpPiD4oT8yfxi4qXoYZg9xsgvJaaRblR5HqlcV3AmNmZz/BAbsznTtpiy0r1asFHK/EjfyPaT0j/G5qw4qf5k8kr8o358cvtJGeNq3JmYorFhfM/6wBSCW5yJjdmc6T9Zm73Nojajb6hKporoZWS2f4zNWXFS/OllZNT3b83I188qY8zEnYlpNVsz8Wbj7ExszOYMZeIr2Vv/J95Q1UzVoswMUP9GMvL1GhMnxR9lHdfaifpRyciRHoZVY8zEXakzoGtITyub6Y5wJjZmc6b/7vSl7SNr275ZmDcUI69WwntvOMYHpFexORonxR+UGZA/vT705BQ9DL2+M/rVuLdtUPZXrpH3WtghZ2JjNmfab2y1KNVENYNW1hyz9hkr/WNszoqT4o+6juv1oSen6GHojTGzDq/GnZnVKDWIXrz9G1vG3Bg/xMZszrTf2Mo4jv5vWl0522Qyke7In1a+/X/Pj5bMD6Z/qs2ROCn+RG1RTLO+K/GKYOKPYO6ZyhijuLdtonsv8w9dY56pFmdiYzZn2W9sMXKoAMEUYRR/mOIXU2hRCj6of4zNWXFibDLFr6zvqIBUKXRFehgqRT5GDxN3pqiqFhLZ2DkTG7M5078AMZKRo2vKG2plpmqpZGTGZmR3Vpwq2UMd4yx2aCYVwYxBxspZFxP3yqyGydYZzsTGbM70Y5dRVZDQm7bPqqLXa1V/mOyD/Mj8QrJZ/1SbI3FibDIzl8yXah8QlYwc2Zo9xijubRs020JZ9zgO/9qlMXfGD7ExmyNNp1+v1/F+v0vT2F77Vm71tBrJr5pWI93qkkJpyxRalClgb+oX4Wm1vjQJrnk6bcwdGSpsMdsGszNypHOWP5VMhahkZHRNzWa9ODHbduqBEORP5hcjo+hhWDnGTOFPieGlrTOxMXdk2veJRw5gRHzDgZAVhwUq/Vt1IITJsj4Q8h0HQvx9YmNuzFB1+sqsAxiMzE8dCGEyVc+PzC8k+1MHQtQs22ubfZbpqfQBcYfKtavTxvwP4ofYmM2ZtsV0MusARsePsO3Kab4PhPhAiGpj9oEQT6eNuSnTt5iUN3mvrJ6hbIeM+KMedFi9/VTdDmHaztpmU7dOon5H/WDui8wHlVVjzNyfWby9xWTMjVm2xdR+fr22avuJWbso/qhrbGWtnulFfjDbPYxdJU7VbTYmTsifXh96coqeHivHmImF18TG3Jzl1Wl0zQdCYn7qQMjozMUHQn6ucu1f9jDmxvghNmZzSn/G5fnk/yzFlfba+f+ITG9vWpXpXuVPZBPpi/xoyfxg+hfFKbPJtL226fUT+YPihPxh4ta7L1g9DKvGGN2fPZyJjdmcaX/Gpf0MbS0wRQ9kiylEZQUIxZ9If9ZPJB+1QQVApp9K/xibTFtl+wjpYeKU9R1tVTH3ReaDyqoxRvdnhjOxMZsz7cfj0ZvphNlaWL39pGyroBlCJhvJM/0b2XpCeqs2R+NU2X5CWbay/aSufUe2n1aO8UWft5iMuSPTvgBRWeco68orzPq7J3P9TFnPM2s0Zr3ErIVa1NpB1j/GJjPGTJyq94oyxtkMj5lJMXoYVo7xcfgLEMbcmtI+8Ym6P9jKob0xtA/X2kL+ZDKRbqRvxJ/IJtIXxaUl84Ppn2ITjTETp/b/7L2S3SNojFHcevcFq4dh9Ri3OBMbszl+iI3ZnGmHPbJFvFqsUIpDij9MP5DvTMGm108kzxSkIhQ/mLFBNmfFqXKvKGOs9AExUuiKbI2OcYYzsTGbM/2wxwlqg94+2TX0Jk987frT84/Rx2xjMP1k+sdkBCYmzNgwNkfjpPiD4oT8ydoyMooehtExPnzYw5h7UsrEJ5/IyNG1b8jIo/5UMxWiNzNQMjKyORqnSkbOPsv09PrQk1P0MFTG2JnYmJsylImvMHP7rA2zzpmdkXvtWxmlf6MzhEqmQjBrdWZsGJsjcVL96c3o7paRnYmNuSl+iI3ZnNJhj4jKQYBvPxCiHlDY7UBI9QDGLgdC1Pshs434qQMh/haTMTdm6FtMEc9n/E2V9i2btTmvZTLoWqSnhfEnItOL9LUyyJ8ohllMkB8I1E+mf4rN0Tgp/vTuHdT3yC8mXooeBuUebnEmNmZzpn0BoiVaVzDrXWY9qKyBKutS9DZFepX1PLM+ZdZL2dqxbX9FiQkzNsjmrDhV7hUmpqjvUZ9Wr5PRGGc4ExuzOcu+ABERrVPYNuhtj95YTEbu6UWgt/RKf5jsg/zI/EKyzNgwNkfipPjDZDUl/qycoofhOA7/QTVj7owfYmM2R5pOv16v4/1+T5+6KdPq6zVmuolkmClkr20kt3pajeTV6X2mF/nBjA1jczROPX+Y5Qfyp9IHxIRptafTxtyRocLWirc+U3hQ3qpKcajnC2qL/EM6Z80QKpkKUcnIVZujcVJmCCMZOWvfk1H0IJyJjbkp037ZY/Zbf3VGjq6t2n5S+zfiTzVTZczOyMjuaJwUf5Sty4hPrJOdiY25KdN/2eOTlWsfCPGBENbmjgdCnImNuSl+iI3ZnGnT6ZNvmFZHfkQyvSl39QAG4psOhMyeViPdnzgQok7zv/1AiKfTxtyU6Zn45A4HQkYPYCC+4UDIirFp5T95IETdAv32AyHOxMbclGWZ+GTnAyGzDmAgPnkgZOXYMH6uPhCiHHyJrn3bgRBnYmNuyrTfnc5g3oboTYf0tPqYNpGt7A2svskzefTWRVljtT8rx6bSv6tsNjtS4sRUnpFNJk5K/KN+MBn5OPy708bcGj/ExmzO9B+PRzyf+IfBH4/Hn9cYPUgma3N+fvUj80/1PfPnajPjlIl0r/Insjl7bJT+RXFCNntto7HO/o/8QXGKbGV9V+Kl4ExszOYs+/F4BFM4YGwwRRimjVIYYXxv/39tUyl2Kf1T/GEKW7PGpto/xibTlilsMXqYOGV9R0VCpdDV4kxszOYMbTEx2w+I6tuQ0cNk195bVd1aUN7AIxl5lj8rMlVLJSOja0o2q85cKrM3dYyz2KGZVIYzsTGbM+2wx8g6ufo2ZPQw2bWyzlHWlVeYDNqTUfs3MkNYOTaV/qFs3doanblUZm+srV4fenJXnImN2Zzpxy5XVa6ZNzDSw2TXyjpHXVdmfWDWQur6dIY/o5kqQpkZMJViZX1ZmbmoMwRl1pbZzvoR4UxszOb4ITZmc6b9fWIgo3t1AU1pFBuRz60c0ptNd1BRh/E9k0VtIzmlf0zBBPnDTDeRnkwv8gP1T7HJtFWmypEeJk6ZP8i3w98nNuaeTPszLqS81D6zVXkDR3oyOeatz7zBFd9Vf3r+MfpGZwjVTJXxyYwctVe22ZA/KE7In0CfM7Exd2Roi4l5k18Z2X5aeeiA2V5h1jnK1sLodk9PRu2fsu2jHHQYHZtK/xibzBjP2mZj4tS7H/zLHsbcmGk/CvB88l9uPo7+l8sRp61TT2SbsdHKtTLn9ahN60MkF/nA+K74k8lEupG+EX8im7PHRumfYhONMROn9v/svZLdI8wYtzgTG7M5foiN2Zzpv+zBFGEYPQxM4YCxkRVEUNGqWqxQikOZ3kx3S6/gwxTllMIbkp81NtX+MTZnxalyr1TH+PFwJjZme5b9skclI0d6GKpvw54eJoMy2w/VbJ1l5J58i7IFM3uGsGpsqv0bycjXa0ycKvcKspXhTGzM5kz/AkRv+0OwRbdFttAbvGeDkUFt0NteuabEm4mxEhNmhsDIM5kK6YnI/GD0KjZH46T404lT6KAzsTGbU1oTK+sTVk7RU/Exst2zwVQ3mTbqmmp2pbgno/av4o+aqUbWyUr/GJuz4lS9V47Dxy6NuTV+iI3ZHKmw9Xq9jvf7DYsxfzPwpYWuyH6lmMLEAk21IhmlONSijE0kp/SvUuhC8rPHJpJnxoaxORonxR8Xtoy5OUNbTOpbXynhd/yQ2me2lOyD9GRys7efZm33ICrbT6MzhGqmyqhk5KrN0Tix/rxer8f7/XYmNuaODK2JmXVcaPRL18m7ZGTGd9Wfnn+svm86EDI7IyObP3QgxJnYmDsybU3MrOMCfem1b8rIrI2RyrVanVZ87+lFqNXbWf5UMhWCWaszY8PYHIlT5o/XxMbcGD/ExmxO6Yfyns85P/zVtr2SyUQgPQyt75FtxkYrF8lkba5xymJ4jXfPdybeqG0rE8UF9Q/FkvEnu68inytjo/RPtTkSJ+RPhjOxMZsz7Te2mIV6VihARR2mQMLoYWCKDKjIlOmJ/GLatLZQvFGBLIs3MzZITukfKiAx/jD9q4xNtX+MzVlx6t3LzsTGbM60X/ZQ3pwn3779xGS16vYGEwv0lm7lPrn9pPZvxB9m9pfpiGB8YMaGsTsSJ28xGXNjph27/FNhYY7/7Rn5aqvyBo70IJmsDTOr+WRGRr6v8IeZ/SE/Mr+QLDM2jM1inJyJjbkjfoiN2ZzpZ6cvbf/2uVKoCWynfv2vTasjPyKZ3pRbXcaMFLtmT6uR/KppNdKtLimUti5sGXNzpn+fWMkelYycte/JKHoYlNkIowfJzd5+YnzPfEFtkX9I5yx/lAMmn9h+UmeTQZyciY25I+qa+P8fj8e/17ljjEn413Ec/xddkB5iY8z34em0MZvjh9iYzfFDbMzm+CE2ZnP8EBuzOX6IjdkcP8TGbI4fYmM2xw+xMZvzH/3nAELaSx2mAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 288x290.88 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(r, s0_p5, T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "r = Rule(170)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 573.149x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(r, s0_pert, T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x290.88 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(r, s0_p1, T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x290.88 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(r, s0_p3, T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPEAAAD2CAYAAAAHzmGxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAMpUlEQVR4nO2dTZbjtg5G5Zwsod84vYfq/a+gaxEZv1NrcEZKdFQgCP7I5gfdO7RIELaLBUq8kh/P53MDAF3+eHcCADAGkxhAHCYxgDhMYgBxmMQA4jCJAcRhEgOIwyQGEIdJDCDOny2Nf/z48fz58+f2+fm5bdu2fXx8/HvMeu34+vHYue2xzbmthdW+1qclTgQrd++91+J4/bw2kc+wFM/LvZSL19bLz4s5Kx/vM5n13Zz7R76byJiRz+n5fD6svk2T+Ovra/v6+tp2VfPx+C/mWd/cjx1fP7927F+Kc+5r0aKOenEinHO3xo6MUfq8om1Kn6H1ebfk3pKP16/l/Y3mU/q7mvXdWP0j301kzOjn9OvXr2IMltMA4jRV4o+Pj+3379+h/3RetfaqRymexd0qcEuVbc29FtejtQrNyudVFbh1xRkZs+dzKkElBhCHSQwgTtNy+vPzc3s8Hk3L6MgS0GKFZbS3dGuJH1lqtZ6anPu9cxnd+v5G8vFOz2Z9N5E8e5bRI58TF7YAEtN1YWsn8l+xdaui5b+Yx4wK3LttUOpj9ZtdgVsq3uxtJC8f77OM5BPZsvTilOJ6ebRU4NaVY89KowSVGECcpkq8g8gRi+P1uVrksMZoycfrt4LIEc2jFNfL49UiR2lszokBbsLQ1WlEDjuO1weRI5bP3USOlpXUGSoxgDhMYgBxprnTGZfRq24jRXJvzaeWXzTeq0QOK84ZFZGjd8wdKjGAONMubO2oiBzHOCoVeFbF80DkeI/IUcuHLSaAxAydEx9REzms8RE5EDmiY84UOWr5cE4MkJyuc+KdDFego2OoiRy19uc+iByxMa8SOWrVmnNigMQwiQHE6bqL6S7LaESOdUUOLw9FkSPyOZWgEgOIM/RkjyOIHIgcXn9EDj+fyEXQElRiAHG6zol3Vj3/tcZH5EDkiI75DpGjtnpjiwkgMUPP2LJQuwJt9csgcnixM4gcXmw1kaM2Vg0qMYA4TGIAcYbc6SMZl9HKIofVPpPIYbXJIHK0bsluG5UYQJ6hLSZEDjs2IgciR61ty3dc++yoxADiTL8B4syqIofVL5PIEclHWeTwjqmJHCWic4dKDCDOtBsgzqhcgfbaIHKsK3LUjtXGWlXk6Jk3VGIAcZjEAOIMbTFZZFpGK4scs/JB5HiNyFE7FeAuJoDETKvEiBxriRyRfJRFDm/cLCJHdCuXSgwgzmVP9ojwTpHj2CajyNGbDyLHe0WOFpFqh0oMIM70J3tEWOEKtJVH7fVo7i35eP0QOWJjZhA5eirwDpUYQJxpDwWIsEIFbj3Pbcm9FteDPeD2MWufk8oe8ChUYgBxmMQA4kzXLs8gcvhcJXJ4/RE5dESOWpxtoxIDyHNZJV5d5PCOIXKsL3JY7bOJHNGLyFRiAHGmV+IVtpGsPKw+Lf/Jz6wucnj9ETnWFTl6tnCpxADiTKvEK1RgRI5xwcFjJZHj2CaDyNFTgXeoxADiMIkBxJn2My5qIod1LJPIYb22wjaSN+7o55RR5IhAJQYQZ+hnXJRFDitOLRevrZefF/MqkcPLI4PIYb2WUeSIQCUGEKfrZ1wyiBzWGC35eP1WEDmieZTienmsIHJE8skgckSgEgOI0/VkD0QOuw8iR2zMV6mUGUSOfSx+AQIgMUxiAHGGfp941W0k69jdRA4rzhlEDpuVltGROFRiAHEue3j86iJHNJ9afpF4iBx2nHOb3pVGJpGj9B1zYQsgMdMfHo/IgcgRbTu60phRgVc+/42OTyUGEGf6kz12Vhc5au3PfRA5YmO+SuSo9S/l3vMePGZX4J7vmEoMIA6TGECcaU/22EHkWEPk8PLIIHKUXivFqb2HWr+WOBFmfcfbRiUGkGfoyR5HEDkQOaz2V4kc3lgWK4sco/GpxADiTL8BApGjrz8ix71FjpExqMQA4ky7AUJN5PBiZxA5vNgZRI5S/q3vwWOVK9DPJzdAAKSGSQwgztBdTMoih9U+k8hhtUHkiLHSMjoClRhAnOmyByIHIkdrPogcdpxoPyoxgDjTZA81kSOSj7LI4R3LIHKU2tf6RGNEufI7juZGJQYQZ0j2QORYV+SoHauNhcjhc9V3XPoskD0AEjP0g2rKe8Cz8mEPmD3gnjFa/j5rUIkBxGESA4jTtcWUQeSI5KMscnjjZhA5av1a4tR4pciB7AFwQ6bdAKEmcvTmg8iByNE6xmgFZosJIDlDN0AgciBynF9H5Pgex+vTsqopQSUGEOeyq9OIHDavEjm8ONZxRI41KrB3nakElRhAHCYxgDjTt5hURA6vPyIHIkdr/BnbSKWx2GICSM60LSZEju+8U+Sw2mcSObw4EVYSOUpjscUEcBOGtpiURQ6vPyIHIkc0jtenR+Rgiwnghgw92cNCReSw+mcSOY5tEDnWqMCRq/hcnQa4IUxiAHGGHh5/RE3ksF5bYRvJG3f0c0Lk0NpGYosJ4CZ0yR47yiKHl0cGkcN6DZGjLf47KnDp75MLWwCJGfoZlyNqIkc0j1JcL48VRI5IPogcfhyvz2yRo2XFeYZKDCDOtFsRSyByvEfkiOSDyGHH8fpcIXLUcq9BJQYQh0kMIM7Q/cQeq4scVpwziBw2KsvoVbeRIrl7+ZyhEgOIM0273EHkWEPksI5lEjmOcVQq8OiKswSVGECcIe3yCCLHWiKH1z+DyGGNn0HkKOWDdgmQmGk3QCByxMZ8lchR61/Kvec9eCByjK84a1CJAcQZugFCeQ/YyyPDHnDptVKc2nuo9WuJE+Gqff7V94Bbr/RvG5UYQB4mMYA40x5Zi8gRG+tVIoc3lgUix3tFjp5l9A6VGECcIe0SkSM2FiKHz91Fjhq1904lBhBn+jO2VEQOL3YGkaOUf+t78FhhG8nql0XkOMZGuwRIzLRnbKmJHFYbRI4YKhVYUeSInFufoRIDiMMkBhBn6BlbiBx2nHMbRA5EjhojpxZUYgBxumSPDCKHdyyDyFFqX+sTjRHlyu+4VvGURI7ei3vbRiUGkGfaDRA7KiJH7VhtLEQOH0QOn5ZVILIHQHKmPXcakQOR4zjWChVYSeRozfUIlRhAHCYxgDjTHlm7oyJyeONmEDlq/Vri1EDk8Gn5Gyzlw4UtgMRcfj8xIgciRzSO16+nAiuJHC35nKESA4hz2f3EiByIHNE4Xp8RlVJF5IjmU4JKDCDO9FsRVUQOL451HJFjjQr8DpXyFSJH7/e/bVRiAHmYxADiTLufGJEDkSMap9TvriJHNJ8SVGIAcYbuJ1YWOaz2mUQOL06E1UUO75iyyFHKB+0SIDHTn7GFyIHIYfWbLXJ4xxRFjpaVxhkqMYA4l/3IuMVKIsexDSLHGhUYkaO8suOcGCAxTGIAcYYelKcsclhjIHLobCNZx5RFjpbTszNUYgBxpj3Z48zqIof1GiJHW/zVVUoVkaM0Jhe2AG7C0JM9LFREjkg+iBx+HK/P1SKHNUZLPl6/d4gcLe/vDJUYQJyh504fURM5IvkgcthxvD6IHLF8enZGSlCJAcQZqsTsAduoVOBVr0BHcm/Np5ZfNN5Ve8C9q6NtoxIDyMMkBhBn6JG1Fioih3Usk8hxjKOyjJ61bPVYUeSoxalBJQYQZ+gGiCNqIofXP4PIYY2PyLGuyDHy/VOJAcSZ9iPjaiJHrX8p95734IHIMV7xIn1URY69HzdAACRm6FZEZZGj9FopTu091Pq1xIkw4788IsfaIkf074lKDCAOkxhAnOmPrFURObyxLBA5EDm8/ld+NzWoxADiTHvaJSJHGUQORI4avRdTt41KDCDPZVtMFiuJHKX8W9+DxwrbSFa/DCKHF1tN5KjlgewBkJzLf1ANkaOdV1VgZZHDap9B5IhcOzhDJQYQh0kMIM5lP6iGyNEGIodPdpFjZHlOJQYQZ/oPqqmIHKX2tT7RGFGulAVqFU9Z5IjkoyRy1FZHbDEBJGbaD6ohcrSByOFzJ5GjFJctJoCbMP1nXBA5fFaqwMoix6x8VhE5uDoNcGOYxADiTPsZFzWRo9avJU4NRA6fnm2kSD5KIkfv0n3bqMQA8kzXLhE5vo/1DpHj2CajyNGbz4oiR+uYZ6jEAOJM0y4ROb6P9c5tJCuP2uvR3Fvy8fohcsTGfD7RLgFSM6RdInLYY60gclj9EDm0RI7o3y6VGEAcJjGAOEOyByIHIkeNq0QOr7+yyNGzzKcSA4jTJXtkEDm8OBFWFzm8Y4gc64kcaJcAN+bReO74/23b/r4uHQAo8Nfz+fyfdaBpEgPAerCcBhCHSQwgDpMYQBwmMYA4TGIAcZjEAOIwiQHEYRIDiMMkBhDnH8mULe6a/sa9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 288x290.88 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(r, s0_p5, T))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regra 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A regra 1 coloca em 1 apenas células que estão em 0 e seus dois vizinhos também estão em 0. Como vemos abaixo, isso leva a um comportamento final aleatório que depende das condições iniciais."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x144 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(1), s0_pert, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(1), s0_p1, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(1), s0_p3, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(1), s0_p5, 20))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regra 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A regra 2 só preserva pontos com pelo menos dois espaços em branco anteriores e os desloca à esquerda."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x144 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(2), s0_pert, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(2), s0_p1, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(2), s0_p3, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(2), s0_p5, 20))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regra 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A regra 3 liga uma célula se ela estiver desligada e sua vizinha à esquerda também estiver desligada, não importa o valor do vizinha da esquerda. O resultado, como vemos abaixo, é uma combinação de oscilação (com padrão que depende do estado inicial) com deslocamento à direita."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x144 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(3), s0_pert, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(3), s0_p1, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(3), s0_p3, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(3), s0_p5, 20))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regra 4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A regra 4 mantém uma célula ligada apenas se as suas duas vizinhas estão desligadas. Isto leva a um apagamento de grupos de células ligadas consecutivas, seguido pela cópia das células isoladas restantes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA44AAAByCAYAAAAcT49rAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAC9klEQVR4nO3awUlDQRRA0YxYQlybHpL+K8gvwrX28NxHvBhQE/Gc5WMY3m64MGtmdgAAAPCZh1svAAAAwH0TjgAAACThCAAAQBKOAAAAJOEIAABAEo4AAAAk4QgAAEASjgAAACThCAAAQHq85vB+v5/D4fBDqwDAfdi27cPseDzeYBMA+F3btr3NzNPlfM3Mly85nU5zPp+/dTEAuDdrrQ+za95LAPir1lrbzJwu576qAgAAkIQjAAAASTgCAACQhCMAAABJOAIAAJCEIwAAAEk4AgAAkIQjAAAASTgCAACQhCMAAABJOAIAAJCEIwAAAEk4AgAAkIQjAAAASTgCAACQhCMAAABJOAIAAJCEIwAAAEk4AgAAkIQjAAAASTgCAACQhCMAAABJOAIAAJCEIwAAAEk4AgAAkIQjAAAASTgCAACQhCMAAABJOAIAAJCEIwAAAEk4AgAAkIQjAAAASTgCAACQhCMAAABJOAIAAJCEIwAAAEk4AgAAkIQjAAAASTgCAACQhCMAAABJOAIAAJCEIwAAAEk4AgAAkIQjAAAASTgCAACQhCMAAABJOAIAAJCEIwAAAEk4AgAAkIQjAAAASTgCAACQhCMAAABJOAIAAJCEIwAAAEk4AgAAkIQjAAAASTgCAACQhCMAAABJOAIAAJCEIwAAAEk4AgAAkIQjAAAASTgCAACQhCMAAABJOAIAAJCEIwAAAEk4AgAAkIQjAAAASTgCAACQhCMAAABJOAIAAJCEIwAAAEk4AgAAkIQjAAAASTgCAACQhCMAAABJOAIAAJCEIwAAAEk4AgAAkIQjAAAASTgCAACQhCMAAABJOAIAAJCEIwAAAEk4AgAAkIQjAAAASTgCAACQhCMAAABJOAIAAJCEIwAAAEk4AgAAkNbMfP3wWq+73e7l59YBAADghp5n5ulyeFU4AgAA8P/4qgoAAEASjgAAACThCAAAQBKOAAAAJOEIAABAEo4AAAAk4QgAAEASjgAAACThCAAAQHoH3gAn1wWRBacAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1152x144 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(4), s0_pert, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(4), s0_p1, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(4), s0_p3, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(4), s0_p5, 20))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regra 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Na regra 5, uma célula é ligada se as suas duas vizinhas são ligadas, independentemente do valor atual da célula. Isto leva a uma oscilação que depende da condição inicial, com algumas células isoladas continuamente ligadas e grupos de células piscando."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x144 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(5), s0_pert, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(5), s0_p1, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(5), s0_p3, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(5), s0_p5, 20))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regra 6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A regra 6 liga uma célula se a sua vizinha à esquerda está desligada e se sua vizinha à direita tem o estado oposto dela.\n",
    "\n",
    "O comportamente resultante já é bem mais interessante do que para as regras anteriores."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x144 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(6), s0_pert, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(6), s0_p1, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(6), s0_p3, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(6), s0_p5, 20))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regra 7"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A regra 7 liga uma célula desde que a célula da esquerda esteja desligada, a menos que a célula e sua vizinha da direita estejam ligadas simultaneamente."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x144 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(7), s0_pert, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(7), s0_p1, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(7), s0_p3, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(7), s0_p5, 20))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comportamentos"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A explicação do funcionamento de uma regra pode ser bastante complexa, então vamos parar de tentar fazer isso, e vamos apresentar alguns tipos de comportamentos distintos."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regras homogeinizantes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Algumas regras levam a que todas as células tenham constantemente o mesmo valor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x144 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(8), s0_pert, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(8), s0_p1, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(8), s0_p3, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(8), s0_p5, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x144 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(96), s0_pert, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(96), s0_p1, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(96), s0_p3, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(96), s0_p5, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x144 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(249), s0_pert, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(249), s0_p1, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(249), s0_p3, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(249), s0_p5, 20))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regras oscilatórias"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Algumas regras produzem oscilações (como já visto acima)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x144 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(31), s0_pert, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(31), s0_p1, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(31), s0_p3, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(31), s0_p5, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x144 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(91), s0_pert, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(91), s0_p1, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(91), s0_p3, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(91), s0_p5, 20))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Como vemos claramente neste último caso, o comportamento transiente até chegar na oscilação pode ser bastante interessante. Veja ainda as regras abaixo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x144 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(15), s0_pert, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(15), s0_p1, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(15), s0_p3, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA44AAADQCAYAAABImz+OAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAKpUlEQVR4nO3dQY5aSxIFUKrFEv4ft/eA978CWESPu/fAn7Yt1a1ETsIR6XOG1hPkIyMSrp5V8fF8Pi8AAADwmX/97gUAAADQm+AIAABAJDgCAAAQCY4AAABEgiMAAACR4AgAAEAkOAIAABAJjgAAAESCIwAAANH1lYv/+uuv57dv3+I1j8fjy9e53W5fXrPrdVZ89V6V6115nRW7PpsVu9a8ovK+dqj8bLqZ1ueVut1T5Xq6nYM73qtbra/oVju7VH3O3Wr01NqZ9puy0/fM5dKvLrp91+x4n126/S64XC7/ez6ff//8jx/P53P5Fb5///683+/xmo+Pjy9fZ+U9d73Oiq/eq3K9K6+zYtdns2LXmldU3tcOlZ9NN9P6vFK3e6pcT7dzcMd7dav1Fd1qZ5eqz7lbjZ5aO9N+U3b6nrlc+tVFt++aHe+zS7ffBZfL5fF8Pr///I/+qyoAAACR4AgAAEAkOAIAABAJjgAAAESCIwAAAJHgCAAAQPTSHMeJuv1p5B0a/sneL3X7k9CddPtz9hOdOFqg2z1166uqvepUE5fLzHO7W+2sqBrTUmli7XTS7UzepVt/Vq5nWp93GIXjiSMAAACR4AgAAEAkOAIAABAJjgAAAESCIwAAAJHgCAAAQCQ4AgAAEAmOAAAARNdXLn48Hu0Ghe7QbRjrDhMH1RpO/LkT+67ajj3vtg/dBrR366uq/Tq1LlacWjtf6dZ7u0ysnU7URY2q9Uzcz3d/Np44AgAAEAmOAAAARIIjAAAAkeAIAABAJDgCAAAQCY4AAABEgiMAAACR4AgAAEB03f2C3YaE7tBtEOsuBptm0/b9xN6rtmPPu+1DtwHt3fpq2iDpXSae291q5yvdem+XibXTibqoUbWeifv5K2v2xBEAAIBIcAQAACASHAEAAIgERwAAACLBEQAAgEhwBAAAIBIcAQAAiARHAAAAousrF99ut8v9fv/lN+02JHSHboNYd/nTBpu+YuKen9h7lU4dZN7tvjr1VuVenVoXK06snRXdem+XibXTibqoUbWek/bTE0cAAAAiwREAAIBIcAQAACASHAEAAIgERwAAACLBEQAAgEhwBAAAIBIcAQAAiK67X/BPHeK7osPgzneYONi0qr4m7vmJvVfp1DOw23116q3KvTq1LlacWDsruvXeLhNrpxN18X6Va+m2n5+txxNHAAAAIsERAACASHAEAAAgEhwBAACIBEcAAAAiwREAAIBIcAQAACASHAEAAIiur1z8eDy2DKj8U4f4rug2iHWXboNNV1TV18Q9P7H3Kp16Bna7r069NXGQ9C4Tz+1OtbOiW+/tMrF2OlEX71e5lg776YkjAAAAkeAIAABAJDgCAAAQCY4AAABEgiMAAACR4AgAAEAkOAIAABAJjgAAAETXVy6+3W6X+/3+rrX84E8d4rui2yDWXToMNn2FwcTZib1X6dQzsNt9deqtiYOkd6nchx333qluVnXrvV1O/M6vpC7er3It734vTxwBAACIBEcAAAAiwREAAIBIcAQAACASHAEAAIgERwAAACLBEQAAgEhwBAAAILrufsFpQ3wvl15DQnfpNoh1l2mDaif2Q6UTe6/SqWdgp/vq1lcnDZJ+VeVenFg7Kzr13k4nfudXUhfvV7mWlff6bK88cQQAACASHAEAAIgERwAAACLBEQAAgEhwBAAAIBIcAQAAiARHAAAAIsERAACA6PrKxY/HY9xQ3GnrrdRtEOsu0wbVTuuHaqf2X5Vde95tHzrdV7e+6jZIutK0c7tb7azo1Hs7Taudbk6si2792WE9njgCAAAQCY4AAABEgiMAAACR4AgAAEAkOAIAABAJjgAAAESCIwAAAJHgCAAAQHTd/YITh+KeOAB6l06DWHfasV+Vn820fqh2av9VmXhur+h0tnfrq8q9OrEuVpxaOytOPFNO/c6vpC7e793r8cQRAACASHAEAAAgEhwBAACIBEcAAAAiwREAAIBIcAQAACASHAEAAIi2z3FcMW220bT1Vus0T2enTjPgVpgxlZ3af1VOPQc7zXTt1leVe3ViXaw4tXZWnHimnPqdX0ldvN+vrMcTRwAAACLBEQAAgEhwBAAAIBIcAQAAiARHAAAAIsERAACASHAEAAAgEhwBAACIrq9cfLvdLvf7/V1r+cG0objT1lut0yDWXSYOqTWcODu1/6qceA52u6dufVW5VyfWxYpTa2dFt/7bYWLtdKMufh9PHAEAAIgERwAAACLBEQAAgEhwBAAAIBIcAQAAiARHAAAAIsERAACASHAEAAAguu5+wYnDgKuGbk5bb7VOg1h3mTik1nDiz53ae5VOPAe73VO3vqrcqxPrYsWptbOiW//tMLF2utnxGXb7bDr0pyeOAAAARIIjAAAAkeAIAABAJDgCAAAQCY4AAABEgiMAAACR4AgAAEAkOAIAABBdf8ebThsGPHEQa4choe/QbRjrDhOHF0/siSqn9l6lE8/BbvfUra8q9+rEulhxau2smPZbcMXE2ulGXXzus/vyxBEAAIBIcAQAACASHAEAAIgERwAAACLBEQAAgEhwBAAAIBIcAQAAiARHAAAAousrFz8ej7JBl9OGAU8cxDpxiO+KbsNYd+g2PHzFxJ6ocmrvVTrxHOx2T936qnKvTqyLFafWzoppvwVXTKydTrqdybv8yn154ggAAEAkOAIAABAJjgAAAESCIwAAAJHgCAAAQCQ4AgAAEAmOAAAARIIjAAAA0fWVi2+32+V+v79rLS+rGqg5cSDuxDVX6jaMdYeJg2on9kSVU3uv0o4977YP3c72bn1VtV+n1sWKU2vnK916b5eJtdPJqXXxGU8cAQAAiARHAAAAIsERAACASHAEAAAgEhwBAACIBEcAAAAiwREAAIBIcAQAACC67n7BbgMspw0DnjiIddoQ31XdanmHiYNqJ/ZElVN7r9KOPe+2D93O9m59VbVfp9bFilNr5yvdem+XibXTycS6+GzNnjgCAAAQCY4AAABEgiMAAACR4AgAAEAkOAIAABAJjgAAAESCIwAAAJHgCAAAQHR95eLH43HksORpw4AnDmKdNsR3Rbc63uWkQbW7TdzzE3uv0qlnYLf76tZbVft1al2sOLV2vtKt93aZWDudTKkLTxwBAACIBEcAAAAiwREAAIBIcAQAACASHAEAAIgERwAAACLBEQAAgEhwBAAAILq+cvHtdrvc7/d3reUHnYZ7Vq5l4kDciWuu0qmOd5oyqPb/VdXXxD0/sfcqnXoGdruvTr1VuVen1sWKE2tnRbfe22Vi7XRSWRefvZcnjgAAAESCIwAAAJHgCAAAQCQ4AgAAEAmOAAAARIIjAAAAkeAIAABAJDgCAAAQXV+5+PF4tBqi2mm458RhwBMHsXaqv1061fFOEwcYV9XXxD0/sfcqnXoGdruvTr1VuVen1sWKE2tnRbfe22Vi7XTy7s/PE0cAAAAiwREAAIBIcAQAACASHAEAAIgERwAAACLBEQAAgEhwBAAAIBIcAQAAiD5eGRT58fHx38vl8p/3LQcAAIDf6N/P5/Pvn//xpeAIAADAn8d/VQUAACASHAEAAIgERwAAACLBEQAAgEhwBAAAIBIcAQAAiARHAAAAIsERAACASHAEAAAg+gdVDRJ5kMSsvAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(15), s0_p5, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x144 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(79), s0_pert, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(79), s0_p1, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA44AAADQCAYAAABImz+OAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAGw0lEQVR4nO3dwY3bRhiA0VWgEpxz3IO3/wq8ReSc9DA55eJAn6iIIjnie8eFII3+EQf4QMO8jDE+AAAA4Jbf9l4AAAAAxyYcAQAASMIRAACAJBwBAABIwhEAAIAkHAEAAEjCEQAAgCQcAQAASMIRAACAdH3kxd++fRvfv39/0VJe4+vr6+5rfvz48fR7rOXeWma11gzfcT5bzmaN6+GI1vpe995nxtks8a6/C27bcs/Pev5vdS4tfZ8lZjwLZlwzt9nP11t4Jv89xvj91z9exhiLP+jz83P8/PnzgaXt73K53H3NvRkseY+1PLIfM1lrhu84ny1ns8b1cERrfa977zPjbJZ4198Ft22552c9/7c6l5a+zxIzngUzrpnb7OfrLTyTv8YYn7/+0T9VBQAAIAlHAAAAknAEAAAgCUcAAACScAQAACAJRwAAANJDz3FcYstHVxzJWv+l9hJnnfFS5vN6ZnzbmWdz5u9+Vkfb86Ot50i2nM2M+zDjmrnNfr6GO44AAAAk4QgAAEASjgAAACThCAAAQBKOAAAAJOEIAABAEo4AAAAk4QgAAEC67vGhY4zNPuusDwDdcsZr2XKvZpvPjL9j1/ltR/v9ufbO52h7frT1rGG2c2lra+3DVnN2dm3jHc+Co3lmxu44AgAAkIQjAAAASTgCAACQhCMAAABJOAIAAJCEIwAAAEk4AgAAkIQjAAAA6br3Am7x4NzXM+NmPq9nxredeTZn/u4cg9/gMcy2D7Otl2Y//8sdRwAAAJJwBAAAIAlHAAAAknAEAAAgCUcAAACScAQAACAJRwAAAJJwBAAAIF33XsAzxhh3X+Phnc9ZMuO1zLZXZrMN1/lta/0GZ5zfltffO5pxz4/EucT/5exqs103M+7nMzN2xxEAAIAkHAEAAEjCEQAAgCQcAQAASMIRAACAJBwBAABIwhEAAIAkHAEAAEjXvRfA/GZ7WOuWzIa9nfk3eObvDszL2fVe3mk/3XEEAAAgCUcAAACScAQAACAJRwAAAJJwBAAAIAlHAAAAknAEAAAgCUcAAADSde8FcA5jjLuveacHpD7CbGA/S66/d+RMgbm969l11rNpy/18ZsbuOAIAAJCEIwAAAEk4AgAAkIQjAAAASTgCAACQhCMAAABJOAIAAJCEIwAAAOm69wIA4KjO+jBqYH7Or/dyhP10xxEAAIAkHAEAAEjCEQAAgCQcAQAASMIRAACAJBwBAABIwhEAAIAkHAEAAEjXvRcAADMbY+y9hIcd4UHSwP6Odn45m56zZD+fmbE7jgAAACThCAAAQBKOAAAAJOEIAABAEo4AAAAk4QgAAEASjgAAACThCAAAQLruvQAAeHceag3MyvnFv9xxBAAAIAlHAAAAknAEAAAgCUcAAACScAQAACAJRwAAAJJwBAAAIAlHAAAA0nXvBQAAHx9jjM0+ywO9gTWtdX45m47NHUcAAACScAQAACAJRwAAAJJwBAAAIAlHAAAAknAEAAAgCUcAAACS5zgCwCQ84wyYlfNrfu44AgAAkIQjAAAASTgCAACQhCMAAABJOAIAAJCEIwAAAEk4AgAAkIQjAAAA6br3AgCA9Ywx7r7Gg7gBeJQ7jgAAACThCAAAQBKOAAAAJOEIAABAEo4AAAAk4QgAAEASjgAAACThCAAAQBKOAAAAJOEIAABAEo4AAAAk4QgAAEASjgAAACThCAAAQBKOAAAAJOEIAABAEo4AAAAk4QgAAEASjgAAACThCAAAQBKOAAAAJOEIAABAEo4AAAAk4QgAAEASjgAAACThCAAAQBKOAAAAJOEIAABAEo4AAAAk4QgAAEASjgAAACThCAAAQBKOAAAAJOEIAABAEo4AAAAk4QgAAEASjgAAACThCAAAQBKOAAAAJOEIAABAEo4AAAAk4QgAAEASjgAAACThCAAAQBKOAAAAJOEIAABAEo4AAAAk4QgAAEASjgAAACThCAAAQBKOAAAAJOEIAABAEo4AAAAk4QgAAEASjgAAACThCAAAQBKOAAAAJOEIAABAEo4AAAAk4QgAAEASjgAAACThCAAAQBKOAAAAJOEIAABAEo4AAAAk4QgAAEASjgAAACThCAAAQBKOAAAAJOEIAABAEo4AAAAk4QgAAEASjgAAACThCAAAQBKOAAAAJOEIAABAEo4AAAAk4QgAAEASjgAAACThCAAAQLqMMZa/+HL56+Pj48/XLQcAAIAd/THG+P3XPz4UjgAAAJyPf6oKAABAEo4AAAAk4QgAAEASjgAAACThCAAAQBKOAAAAJOEIAABAEo4AAAAk4QgAAED6B9Ro3RQoNx0wAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(79), s0_p3, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(79), s0_p5, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x234.985 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(94), s0_pert, 40))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 702.439x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(94), s0_p1, 40))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(94), s0_p3, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(94), s0_p5, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA44AAAByCAYAAAAcT49rAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAADh0lEQVR4nO3dwW0bQQyGUTFICco56kHqvwJtEbm7h/F5OcqPrBFHjua948AwdDM+06RrjHECAACA3/n27A8AAADA1yYcAQAAiIQjAAAAkXAEAAAgEo4AAABEwhEAAIBIOAIAABAJRwAAACLhCAAAQPT9yBefz+dxuVw+6aMAwNewbdv0dr1en/BJAODf2rbtbYzxo7/XGOOPv8ntdhv3+/2vfjAA+Gqqano78vMSAP5XVbWNMW793Z+qAgAAEB2aOFaVX7cC8HI+Mk18NJUEgBdg4ggAAMBxwhEAAIBIOAIAABAJRwAAAKJD/8cRAFbg33EAwJ6JIwAAAJFwBAAAIBKOAAAARHYcAaCxzwgAeyaOAAAARMIRAACASDgCAAAQCUcAAAAix3EAoKmq6c3BHABWZuIIAABAJBwBAACIhCMAAACRHUcAaOwzAsCeiSMAAACRcAQAACASjgAAAETCEQAAgMhxHABoqmp6czAHgJWZOAIAABAJRwAAACLhCAAAQGTHEQAa+4wAsGfiCAAAQCQcAQAAiIQjAAAAkXAEAAAgchwHAJqqmt4czAFgZSaOAAAARMIRAACASDgCAAAQ2XEEgMY+IwDsmTgCAAAQCUcAAAAi4QgAAEAkHAEAAIgcxwGApqqmNwdzAFiZiSMAAACRcAQAACASjgAAAER2HAGgsc8IAHsmjgAAAETCEQAAgEg4AgAAEAlHAAAAIsdxAKCpqunNwRwAVmbiCAAAQCQcAQAAiIQjAAAAkR1HAGjsMwLAnokjAAAAkXAEAAAgEo4AAABEwhEAAIDIcRwAaKpqenMwB4CVmTgCAAAQCUcAAAAi4QgAAEBkxxEAGvuMALBn4ggAAEAkHAEAAIiEIwAAAJFwBAAAIHIcBwCaqpreHMwBYGUmjgAAAETCEQAAgEg4AgAAENlxBIDGPiMA7Jk4AgAAEAlHAAAAIuEIAABAJBwBAACIHMcBgKaqpjcHcwBYmYkjAAAAkXAEAAAgEo4AAABEdhwBoLHPCAB7Jo4AAABEwhEAAIBIOAIAABAJRwAAACLHcQCgqarpzcEcAFZm4ggAAEAkHAEAAIiEIwAAANHRHce30+n06zM+CAA8y6Odxo98DQC8gJ+PHsuyPwAAAIk/VQUAACASjgAAAETCEQAAgEg4AgAAEAlHAAAAIuEIAABAJBwBAACIhCMAAACRcAQAACB6BxShZdbNV6QOAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1152x144 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(201), s0_pert, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(201), s0_p1, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(201), s0_p3, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(201), s0_p5, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x144 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(156), s0_pert, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(156), s0_p1, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(156), s0_p3, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(156), s0_p5, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x144 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(190), s0_pert, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA44AAADQCAYAAABImz+OAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAJoElEQVR4nO3dQZLjxhUE0E8HjyCtrTuw738C9iG8tu8AraSwxsMkaKHRCeK9JQNBZlWBjMnARP/LsiwDAAAAj/zjuwMAAADQTXEEAAAgUhwBAACIFEcAAAAixREAAIBIcQQAACBSHAEAAIgURwAAACLFEQAAgOj6ysW//PLL8ttvv8VrPj8/n77P7XZ75WMBdvHs98tv1/tx5vyM++Ix/847n63O3L3z9TY8q/8sy/Lrj69flmVZHebj42O53+/xmsvl8vR9XvlMgL08+/3y2/V+nDk/4754zL/zzmerM3fvfL0Nz+pzWZaPH1/3X1UBAACIFEcAAAAixREAAIBIcQQAACBSHAEAAIgURwAAAKKXxnFcLpfd/kauP8cLbGnNn6jegt+uHs6cn3FfPLbX3swcc3/e0Z5nvpWz3js7n5VxHAAAALxOcQQAACBSHAEAAIgURwAAACLFEQAAgEhxBAAAIFIcAQAAiBRHAAAAout3fOiawZ1rhlyedQAo8FdNA739du3DmfMz7ovH9hwefsT9eUc7D4zfxFnvnaOclSeOAAAARIojAAAAkeIIAABApDgCAAAQKY4AAABEiiMAAACR4ggAAECkOAIAABBdt37DrQZ3rvGOA0CBv2oaWu23ax/OnJ9xX/y999mKf+d1OMrA+P921nvniGf1iCeOAAAARIojAAAAkeIIAABApDgCAAAQKY4AAABEiiMAAACR4ggAAECkOAIAABBdX7n4drvN/X6P1xxxCO1Zh8fCdzvi78UWzvzb5cwfe9czX8N98dhZ92bmvN+bIw6Mf8d7p21NDTxxBAAAIFIcAQAAiBRHAAAAIsURAACASHEEAAAgUhwBAACIFEcAAAAixREAAIDo8spQ1MvlstsE1aahm0cbHAsNjjbodytNWWb2/f1qW5cz79C2dvfFY/J8vSMOjD/iWR1xn/eycv8+l2X5+PF1TxwBAACIFEcAAAAixREAAIBIcQQAACBSHAEAAIgURwAAACLFEQAAgEhxBAAAILp+x4e2De58lmdNlraBy/CVmr6fMwZ6J1v9fh1xXVtoyjKz75mvccS1b6Epy4w8z2yRp21NW2lbV1ueo/nq/fPEEQAAgEhxBAAAIFIcAQAAiBRHAAAAIsURAACASHEEAAAgUhwBAACIFEcAAACi69Zv2Da4c688ew5chq/0jt/PtZ7lacoys12ed13XGs68g/visaPtzcx75mn7zqxx1rN6Vw3754kjAAAAkeIIAABApDgCAAAQKY4AAABEiiMAAACR4ggAAECkOAIAABApjgAAAETXVy6+3W5zv9/jNWcdJLpVljXvA/+vs34/Z7ryNGXZUtu6mvI0Zdlb29qb8jRlmZHnSNr2pi3P0Rxl/zxxBAAAIFIcAQAAiBRHAAAAIsURAACASHEEAAAgUhwBAACIFEcAAAAixREAAIDo8srA+cvlstt0+qZBmE1ZZtbl4Xza7sGz5mnKsqW2dTXlacqyt7a1N+VpyjIjz5G07U1bnqNp27+VeT6XZfn48XVPHAEAAIgURwAAACLFEQAAgEhxBAAAIFIcAQAAiBRHAAAAIsURAACASHEEAAAgun7Hhx5tEGZTlpl1eda8D8dxxHtwK015mrJsqW1dTXmasuytbe1NeZqyzMhzJG1705bnaNr276vzeOIIAABApDgCAAAQKY4AAABEiiMAAACR4ggAAECkOAIAABApjgAAAESbz3E82zyTV+yZxazH4zjr92HmeHmOOMvqaHs805XniGe+xtHOYaYrT1OWmXPnadK2N215jqZt/xryeOIIAABApDgCAAAQKY4AAABEiiMAAACR4ggAAECkOAIAABApjgAAAESKIwAAANH1lYtvt9vc7/d4zdkGYf6hKcvMdnnWvA+PHfHMtyLP12tbkzwd2tYtz2NNWWb68jRp25u2PEf0bA+d5//yxBEAAIBIcQQAACBSHAEAAIgURwAAACLFEQAAgEhxBAAAIFIcAQAAiBRHAAAAossrA94vl8tu0+CbBmE2ZZk5Zp531LbH8mQNg3Nf0bYmeTq0rVuex5qyzPTlaWMY/Htp2sOmLDOr83wuy/Lx4+ueOAIAABApjgAAAESKIwAAAJHiCAAAQKQ4AgAAECmOAAAARIojAAAAkeIIAABAdP2ODz3aIMymLDPHzLPmfdoYDPvYmfNsoW1N8nRoW7c8jzVlmenL06Zpf5qyHFXTHjZlmfn6PJ44AgAAECmOAAAARIojAAAAkeIIAABApDgCAAAQKY4AAABEiiMAAACR4ggAAEB03foNzzYI8xVNWWb2zbPmfdbk2Yozf+zMebbQtiZ5OrStW57sWZ6mLDPv+Z1Zq2l/mrIcVdMeNmWZ6cjjiSMAAACR4ggAAECkOAIAABApjgAAAESKIwAAAJHiCAAAQKQ4AgAAECmOAAAARNdXLr7dbnO/3+M1ZxuE+YemLDPvm6dpXU1ZZuTZQ9ua5OnQtm55sqY8TVkaNe1PU5ajatvDZ3massx03F+eOAIAABApjgAAAESKIwAAAJHiCAAAQKQ4AgAAECmOAAAARIojAAAAkeIIAABAdFkzcPLPiy+X9Rf/TU2DMJuyzMizF4NhH2vLsxVn/lhbnr20rVuerClPU5ZGbfvT9Pt/REc7z5nz/haszPO5LMvHj6974ggAAECkOAIAABApjgAAAESKIwAAAJHiCAAAQKQ4AgAAECmOAAAARIojAAAA0fU7PvRogzCbssycO89WmtbVlGWmL89WmtbVlGWmL8+e/P4/Js9jTVkate1PW56jadu/pjxNWWa+Po8njgAAAESKIwAAAJHiCAAAQKQ4AgAAECmOAAAARIojAAAAkeIIAABApDgCAAAQXbd+w7MNwnxFU5aZvjxbaVpXU5aZvjxbaVpXU5aZvjx7alp7U5YZeZ55luddvzNrHO2sZs59Xs+07V9TnqYsMx15PHEEAAAgUhwBAACIFEcAAAAixREAAIBIcQQAACBSHAEAAIgURwAAACLFEQAAgOj6ysW3223u93u85myDMP/QlGWmL89WmtbVlGWmL89WmtbVlGWmL8+emtbelGVGnmfa8jRp25u2PEfTtn9Hy9OUZabjXvfEEQAAgEhxBAAAIFIcAQAAiBRHAAAAIsURAACASHEEAAAgUhwBAACIFEcAAACiy5qBk39efLn8e2b+9XVxAAAA+Eb/XJbl1x9ffKk4AgAAcD7+qyoAAACR4ggAAECkOAIAABApjgAAAESKIwAAAJHiCAAAQKQ4AgAAECmOAAAARIojAAAA0e81Qbj9YSmMJgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(190), s0_p1, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(190), s0_p3, 20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA44AAADQCAYAAABImz+OAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAJa0lEQVR4nO3dQW7jRhAFUCnQESbrzB3s+5/APkTWyR2Y3SBxoC8ablO/m+8tDUKsrm7J+qDhum7bdgEAAIB7fnt2AQAAAHQTHAEAAIgERwAAACLBEQAAgEhwBAAAIBIcAQAAiARHAAAAIsERAACASHAEAAAgun3m4h8/fmw/f/6M17y/vz98nZeXl4fXjHqdPR7d68h697zOHqN6s8eomvc4cl0jHNmbNrO9z4/UtqYj62n7HBxxr7azvkfb2RnlqD63ndFVz85s3ymbfs9cLn3nou13zYj7jNL2veByufy9bdvvH3943bZt9yu8vr5ub29v8Zrr9frwdfbcc9Tr7PHoXkfWu+d19hjVmz1G1bzHkesa4cjetJntfX6ktjUdWU/b5+CIe7Wd9T3azs4oR/W57YyuenZm+07Z9Hvmcuk7F22/a0bcZ5S27wWXy+V927bXjz/0p6oAAABEgiMAAACR4AgAAEAkOAIAABAJjgAAAESCIwAAANGnxnFcr9eu/7t9Um3/wnqUpn+pvUfbv90+UtvZadLWm7Z6Rplt1MYoM44zKfw384dwdo6511mt+l1wRW093lmPcRwAAAB8nuAIAABAJDgCAAAQCY4AAABEgiMAAACR4AgAAEAkOAIAABAJjgAAAES3ZxfAfx05JLRw2OiQexl4+zV6c19bb9rqGaVpUPmq+9n2mTybtvfeqmfnrLw/59H2fvjuejxxBAAAIBIcAQAAiARHAAAAIsERAACASHAEAAAgEhwBAACIBEcAAAAiwREAAIDo9uwCzqRtSOgobetqq6eJ3mRnHQZ/pLMOKj/rumd11s8CZ+f76fE82vaqoR5PHAEAAIgERwAAACLBEQAAgEhwBAAAIBIcAQAAiARHAAAAIsERAACASHAEAAAguj27gFU0DOX8Dm3raqunid5kTf1pqmWksw4qP+u6Z9XUQ2dnLXo8l0f75fvt/3niCAAAQCQ4AgAAEAmOAAAARIIjAAAAkeAIAABAJDgCAAAQCY4AAABEgiMAAADR7dkFzGCWoZyf1bautnqa6E3W1J+mWkY666Dys657Vk09dHbWosdzadqvplq+yhNHAAAAIsERAACASHAEAAAgEhwBAACIBEcAAAAiwREAAIBIcAQAACASHAEAAIhuzy6gwaPBnLMM5fy3tmGjbfU00ZusqT9NtYx05kHlR33+t617Rk09PPN7ZlUrfhdcVdN7oqmWI3jiCAAAQCQ4AgAAEAmOAAAARIIjAAAAkeAIAABAJDgCAAAQCY4AAABEgiMAAADR7dkFfLcVB3O2ramtniZ6k7X1Z8UB0GceVH5UPW3rnlFbD4/6LGhb96r0eR5Ne9VUSwtPHAEAAIgERwAAACLBEQAAgEhwBAAAIBIcAQAAiARHAAAAIsERAACASHAEAAAguj27gK9YcTBn25ra6mmiN1lbf9rqGeHINbX176h62tY9o7YeOjtr0ed5tO3Vo3qcm//zxBEAAIBIcAQAACASHAEAAIgERwAAACLBEQAAgEhwBAAAIBIcAQAAiARHAAAAotuzC7inbUjoCG1raqunjcGw97WdnbZ6RjhyTW39a1r7bOfmaGc9O23rXpU+z6Ntr9rqWYUnjgAAAESCIwAAAJHgCAAAQCQ4AgAAEAmOAAAARIIjAAAAkeAIAABAJDgCAAAQ3Z5x0xWHcratqa2eNvpzX1tv2uoZoWnA/ch77XHmtc+mrX9NZ8e5+bq288V9bXvVVs+ZeOIIAABAJDgCAAAQCY4AAABEgiMAAACR4AgAAEAkOAIAABAJjgAAAETD5ziuOFulbU1t9bTRn/vaetNWzwhNs+ZG3muPM699Nm39c3bWosfzaNurtnr4L08cAQAAiARHAAAAIsERAACASHAEAAAgEhwBAACIBEcAAAAiwREAAIBIcAQAACC6febil5eXy9vbW7xmxqGcj4aNGnzaQ3/ua+tNWz0jnHlI+ZnXPpu2/jk7a9HjebTtVVs9fJ4njgAAAESCIwAAAJHgCAAAQCQ4AgAAEAmOAAAARIIjAAAAkeAIAABAJDgCAAAQXfcM4/x18fW6/+ISTcNGm2pppD/3tfWmrZ5RHq1r1SHlBrTPo61/zs5a9HgebXvVVg/37dyr923bXj/+3BNHAAAAIsERAACASHAEAAAgEhwBAACIBEcAAAAiwREAAIBIcAQAACASHAEAAIhuzy7gK5qGjTbV0kh/7mvrTVs9oxy1rrb+GdA+j7b+OTtr0eN5tO1VWz3c99175YkjAAAAkeAIAABAJDgCAAAQCY4AAABEgiMAAACR4AgAAEAkOAIAABAJjgAAAES3ZxdwT9Ow0aZaGunPfW29aatnlKPW1dY/A9rn0dY/Z2ctejyPtr1qq4f7GvbKE0cAAAAiwREAAIBIcAQAACASHAEAAIgERwAAACLBEQAAgEhwBAAAIBIcAQAAiG7PuGnDAMt/e1TPmQeftu1Vk7betNUzStOg8lX3c9Wzc5S2/jk7a9HjebTtVVs93DfLXnniCAAAQCQ4AgAAEAmOAAAARIIjAAAAkeAIAABAJDgCAAAQCY4AAABEgiMAAADRbfQLtg2wbKunid5kZx0Gf6SzDio/67pn1NY/Z2ctejyPtr1qq4f7VtorTxwBAACIBEcAAAAiwREAAIBIcAQAACASHAEAAIgERwAAACLBEQAAgEhwBAAAILp95uKXl5fL29tbvMbw0w56kzX1p6mWkc46qPys657Vox6u+jvN2fl+ejyXs34W8DVn2ytPHAEAAIgERwAAACLBEQAAgEhwBAAAIBIcAQAAiARHAAAAIsERAACASHAEAAAguu4ZXPnr4ut1/8VfdLaBmp+hN1lTf5pqGemsg8rPuu5ZNfXQ2VmLHs+lab+aaiFbda92rut927bXjz/3xBEAAIBIcAQAACASHAEAAIgERwAAACLBEQAAgEhwBAAAIBIcAQAAiARHAAAAotszbrrqQM0R9CZr6k9TLSOdeVD5o3pWXfeMmnp45vfMqo76LODrmt4TTbXw2Irv8+8+g544AgAAEAmOAAAARIIjAAAAkeAIAABAJDgCAAAQCY4AAABEgiMAAACR4AgAAEB03TMo8tfF1+tfl8vlz+8rBwAAgCf6Y9u23z/+8FPBEQAAgPPxp6oAAABEgiMAAACR4AgAAEAkOAIAABAJjgAAAESCIwAAAJHgCAAAQCQ4AgAAEAmOAAAARP8AerqZ8dUOgwsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1152x241.92 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(190), s0_p5, 20))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regularidades elaboradas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Algumas regras geram comportamentos com regularidades elaboradas, de difícil descrição."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA4EAAAD0CAYAAAAlrSMjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAJiElEQVR4nO3dQXLcNhQE0K9UjuCsozvI9z+BfQdnHd1hskhlYQU2MTAJguz3dh6xy9xNdUlAvzwejwIAACDDb2e/AAAAAPMogQAAAEGUQAAAgCBKIAAAQBAlEAAAIIgSCAAAEEQJBAAACKIEAgAABFECAQAAgvz+zMOfPn16vL6+HvQqADDX169fv/v329vbSW8CAPv69u1bvb+/v7R+9lQJfH19rS9fvuzzVgBwspeX778bfccBcBefP3/+4c/8OSgAAECQl8fj0f/wy0v/wwCwkJ7vu4+/GQSAK3s8Hs0vNr8JBAAACKIEAgAABFECAQAAgiiBAAAAQZ6aiHh7e3N9NgCX1Lr0peeymGcuUAOAVZiIAAAAoKqUQAAAgChKIAAAQBBj8QDc0sg4fCtjQB6AqzIWDwAAgBIIAACQRAkEAAAIogQCAAAEMRYPwC31XPry8bOeS2CMxwNwBcbiAQAAqColEAAAIIoSCAAAEMRYPAC3sPV91jrv13MmcOTcIACswFg8AAAASiAAAEASJRAAACCInUAAbmFrF7B1ZrBnS3DrDKDdQABWZCcQAACAqlICAQAAoiiBAAAAQZRAAACAIMbiAbicnu+unktftjI9/7fxeABWZSweAAAAJRAAACCJEggAABDEWDwAl9M6h7c1Dt+TaRk5A2hAHoCzGYsHAACgqpRAAACAKEogAABAECUQAAAgiLF4AJY3axy+ldm6CGYkAwAzGIsHAABACQQAAEiiBAIAAAQxFg/A8nrO7m2Nuo9kWozHA3AFxuIBAACoKiUQAAAgihIIAAAQxE4gAMvZ+m5qncPbIzP6zB4ZANibnUAAAACUQAAAgCRKIAAAQBAlEAAAIIixeACWszX03roE5ohM65mP9soAwJ6MxQMAAFBVSiAAAEAUJRAAACCIsXgATtXzPdRzdu+ITIvxeACuwlg8AAAASiAAAEASJRAAACCInUAATtU6H7e18XdUpmXWGUDbgQDsyU4gAAAAVaUEAgAARFECAQAAgiiBAAAAQYzFAzDVyuPwrczWpS6zMgDwLGPxAAAAKIEAAABJlEAAAIAgxuIBmKrnHN7W2PqsTIvxeACuwFg8AAAAVaUEAgAARFECAQAAgiiBAAAAQYzFA3CYkcH2ntxRmdFnzsoAwM8YiwcAAEAJBAAASKIEAgAABDEWD8Bhes7Ytc7ybQ29z8q0nvloVuZHOQBoMRYPAABAVSmBAAAAUZRAAACAIHYCAdjNyC7gypmWs3YDe3MA8B87gQAAACiBAAAASZRAAACAIEogAABAEGPxAOym5zKWnktStobej8q0nHURjPF4AH6FsXgAAACqSgkEAACIogQCAAAEMRYPwLCt75DRc3grDcpvnc2blWnljMcD8DPG4gEAAFACAQAAkiiBAAAAQZRAAACAIMbiARi2dbFKzwUoI4PyszItZw7Bj1w4A0AmY/EAAABUlRIIAAAQRQkEAAAIYiwegC6zBtt7ckdlRp+5UgaAHMbiAQAAUAIBAACSKIEAAABB7AQC0KXnvNzIGbuRLcFZmdYzH83KtHKje4MA3J+dQAAAAKpKCQQAAIiiBAIAAARRAgEAAIIYiwegadY4/MqZlrOG4HtyoxfOAHBPxuIBAABQAgEAAJIogQAAAEGMxQPQ1HOmbuus20im9cysTMtZZwCNxwPwK4zFAwAAUFVKIAAAQBQlEAAAIIgSCAAAEMRYPABVtX1hyMjFKqOXsaw0KH/EQPvoqPusy2MAuAdj8QAAACiBAAAASZRAAACAIMbiAaiq7fNxPefY9si0PjtzuH6VTE9urwwA12csHgAAgKpSAgEAAKIogQAAAEHsBAIEWnmrryd3VGb0mbtnALgmO4EAAAAogQAAAEmUQAAAgCBKIAAAQBBj8QCBei5AGbk0ZY9MK3fmcP2sgfaVLoIxIA9wfcbiAQAAqColEAAAIIoSCAAAEMRYPECAlcfhV860nHkub6XziQCsz1g8AAAASiAAAEASJRAAACCIEggAABDEWDxAgJ5LUrYuL5mVaT0zK9Ny1kUwK2cAWJ+xeAAAAKpKCQQAAIiiBAIAAAQxFg9wM6Oj6Fu5WZlW7szMSgPtK58bBGA9xuIBAABQAgEAAJIogQAAAEHsBALczMiGXit3Vqb12ZmbhatkenJnnk8EYC12AgEAAKgqJRAAACCKEggAABBECQQAAAhiLB7g4q42vr6V6ckdlRl9Ji3TmwPgXMbiAQAAUAIBAACSKIEAAABBjMUDXNxeo+hbQ++zMq3cmcP1Kw+0r5wB4FzG4gEAAKgqJRAAACCKEggAABBECQQAAAhiLB7gYo4YUm/lZNpWHmhf/ZIaAOYyFg8AAIASCAAAkEQJBAAACGIsHuBijhpF3zrjNSvTemZWpuVKA+2rn08EYB5j8QAAAFSVEggAABBFCQQAAAhiJxBgYTP38I7YH7zDZuHVt/lWzgBwLDuBAAAAKIEAAABJlEAAAIAgSiAAAEAQY/EAC5s1pN7KnZVpfXbmcP0qmZ7c1S6pAeA4xuIBAACoKiUQAAAgihIIAAAQxFg8wEKuNqR+RKYnd1Rm9Jm0TE9u9KwhAPsxFg8AAIASCAAAkEQJBAAACGInEGAhZ+7hHbE/eIfNwrtt862cAWA/dgIBAACoKiUQAAAgihIIAAAQRAkEAAAIYiwe4CQrDam3cjJtdxtoX/2SGgDGGYsHAABACQQAAEiiBAIAAAQxFg9wkpWG1FufJQ7Xt1xpbP3q5xN/lAPgecbiAQAAqColEAAAIIoSCAAAEEQJBAAACGIsHmCS1UfRjxihv8NwfeJA+8oXzgDQz1g8AAAASiAAAEASJRAAACCIsXiASVYeUu95v9Th+lUyPbmE84kA9DEWDwAAQFUpgQAAAFGUQAAAgCB2AgEOkrChd0SmJ3dUZvSZtExPbuZZQwDa7AQCAACgBAIAACRRAgEAAIIogQAAAEGMxQMc5EpD6j3vlzpcb6B9/QtnAPg/Y/EAAABUlRIIAAAQRQkEAAAIYiweYAdXH1Jv5WTarnZeLvF8IgD/MhYPAACAEggAAJBECQQAAAiiBAIAAAQxFg+wg6sPqfe8X8JwfcvKF6Dc7ZKaVm70/QDSGYsHAACgqpRAAACAKEogAABAkGfH4v+uqr+Oex0AAAB28Ofj8fij9YOnSiAAAADX5s9BAQAAgiiBAAAAQZRAAACAIEogAABAECUQAAAgiBIIAAAQRAkEAAAIogQCAAAEUQIBAACC/AMD5Pxx+qCt2QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1135.06x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(57), s0_pert, 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 564.706x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(57), s0_p1, 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 564.706x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(57), s0_p3, 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 564.706x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(57), s0_p5, 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1135.06x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(62), s0_pert, 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 564.706x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(62), s0_p1, 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 564.706x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(62), s0_p3, 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 564.706x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(62), s0_p5, 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1135.06x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(118), s0_pert, 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 564.706x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(118), s0_p1, 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 564.706x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(118), s0_p3, 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 564.706x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(118), s0_p5, 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1135.06x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(214), s0_pert, 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 564.706x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(214), s0_p1, 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 564.706x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(214), s0_p3, 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 564.706x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(214), s0_p5, 50))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comportamentos fractais"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Algumas regras têm comportamento similar a fractais a perturbações."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 573.149x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(18), s0_pert, 100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 564.706x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(18), s0_p1, 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 564.706x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(18), s0_p3, 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 564.706x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(18), s0_p5, 50))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Veja como o comportamento fractal a perturbação gera um comportamento extremamente complexo a condições com várias células inicialmente ligadas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1135.06x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(90), s0_pert, 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 564.706x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(90), s0_p1, 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 564.706x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(90), s0_p3, 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 564.706x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(90), s0_p5, 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1135.06x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(60), s0_pert, 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 564.706x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(60), s0_p1, 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 564.706x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(60), s0_p3, 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 564.706x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(60), s0_p5, 50))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Algumas regras, como a 218 abaixo, perdem o comportamento fractal dependendo da densidade."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1135.06x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(218), s0_pert, 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 564.706x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(218), s0_p1, 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 564.706x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(218), s0_p3, 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 564.706x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve(Rule(218), s0_p5, 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}