{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Criticalidade"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "No estudo de física estatística é comum ser introduzido o conceito de **estados críticos**. Esses estados ocorrem durante o processo de transição de fase. Por exemplo, na transição de líquido para sólido, ou na magnetização de um material. Essas transições costumam ser bruscas com a alteração de um parâmetro, como a temperatura nos exemplos anteriores, que é chamado o **parâmetro de controle**. A fase por sua vez é avaliada por um **parâmetro de ordem**, como a magnetização.\n",
    "\n",
    "Conceitos similares ocorrem em vários sistemas complexos, e têm uma grande importância pois têm efeito significativo no comportamento do sistema.\n",
    "\n",
    "Veremos abaixo alguns exemplos"
   ]
  },
  {
   "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": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numba import njit, jit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Modelo de trafego com a regra elementar 184"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Autômatos celulares têm também sido usados para modelar de forma simplificada certos sistemas reais. A idéia é tentar capturar comportamentos típicos de sistemas reais usando-se modelos o mais simples possíveis.\n",
    "\n",
    "Lembremo-nos do comportamento da regra 184."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def evolve_184(initial_state, num_steps):\n",
    "    table = [0, 0, 0, 1, 1, 1, 0, 1]\n",
    "    n = initial_state.size\n",
    "    evolution = np.zeros((num_steps + 1, n + 2), dtype=np.int)\n",
    "    evolution[0, 1:-1] = initial_state\n",
    "    evolution[0,  0] = initial_state[-1]\n",
    "    evolution[0, -1] = initial_state[ 0]\n",
    "    for t in range(num_steps):\n",
    "        for i in range(1, n+1):\n",
    "            evolution[t+1, i] = table[evolution[t, i-1]*4 + evolution[t, i]*2 + evolution[t, i+1]]\n",
    "        evolution[t+1,  0] = evolution[t+1, -2]\n",
    "        evolution[t+1, -1] = evolution[t+1,  1]\n",
    "    return evolution[:, 1:-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def init_perturbation(n, perturbation_state=1):\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] = perturbation_state\n",
    "    return res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_evolution(evolution, ax=None):\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",
    "    if ax is None:\n",
    "        ax = plt.gca()\n",
    "    ax.matshow(evolution, cmap='binary')\n",
    "    ax.set_aspect('equal')\n",
    "    ax.set_xticks([])\n",
    "    ax.set_yticks([])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Partindo de uma célula ligada à esquerda\n",
    "s0 = np.zeros(50, dtype=np.int)\n",
    "s0[0] = 1\n",
    "plot_evolution(evolve_184(s0, 50))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note como a célula ocupada vai se deslocando uma casa para a direita a cada passo de tempo. Se tivermos mais de uma célula, mas isoladas, isso irá acontecer independentemente para todas as células (lembre-se das condições de contorno periódicas)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Partindo de 5 células ligadas\n",
    "s0 = np.zeros(50, dtype=np.int)\n",
    "s0[[0, 10, 20, 30, 40]] = 1\n",
    "plot_evolution(evolve_184(s0, 50))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Isso indica que podemos considerar esse modelo como representando veículos se deslocando para a direita com a mesma velocidade.\n",
    "\n",
    "Vamos agora ver o que acontece se temos células consecutiva ocupadas (veículos sem espaço entre eles)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s0 = np.zeros(50, dtype=np.int)\n",
    "s0[[0, 1, 10, 11, 12, 30, 31, 32, 33, 34]] = 1\n",
    "plot_evolution(evolve_184(s0, 50))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note como os veículos mais atrás nos conjuntos de veículos esperam que haja espaço antes deles para começar a andar, como no tráfego real. \n",
    "\n",
    "Vamos agora definir a *velocidade média* dos veículos no instante $t$ da seguinte forma: se o veículo $i$ conseguiu se deslocar para a direita no instante $t+1$, então contabilizamos a velocidade desse veículo como 1; se ele ficou parado, contabilizamos sua velocidade como 0. Fazemos então a média das velocidades de todos os veículos. Essa média estará entre 0 e 1.\n",
    "\n",
    "Vejamos inicialmente o que acontece para diferentes densidade de veículos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve_184(init_random(100, 0.02), 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve_184(init_random(100, 0.1), 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve_184(init_random(100, 0.25), 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve_184(init_random(100, 0.4), 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve_184(init_random(100, 0.5), 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve_184(init_random(100, 0.6), 50))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_evolution(evolve_184(init_random(100, 0.75), 50))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "À medida que a densidade aumenta, aumenta a presença de grupos consecutivos de veículos, e como apenas o primeiro veículo de cada grupo consegue andar em cada instante, a velocidade média vai decaindo.\n",
    "\n",
    "Vamos calcular numericamente a velocidade média de cada configuração contando o número de células ocupadas que são precedidade por uma célula livre (número de veículos que andam) e dividindo pelo número total de células ocupadas (número total de veículos)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mean_velocities(evolution):\n",
    "    \"\"\"Compute the mean velocities of an evolution, for each time\"\"\"\n",
    "    ntimes = evolution.shape[0]\n",
    "    velocities = np.zeros(ntimes)\n",
    "    next_cell = np.arange(1, evolution.shape[1]+1)\n",
    "    next_cell[-1] = 0\n",
    "    nvehicles = np.count_nonzero(evolution[0, :] == 1)\n",
    "    for t in range(ntimes):\n",
    "        cell_occupied = evolution[t, :] == 1\n",
    "        next_cell_free = evolution[t, next_cell] == 0\n",
    "        velocities[t] = np.count_nonzero(np.logical_and(cell_occupied, \n",
    "                                                        next_cell_free)) / nvehicles\n",
    "    return velocities"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Estamos interessados apenas na velocidade de equilíbrio (depois de as características especiais das condições iniciais forem estabilizadas), portanto simularemos por um certo número de intervalos de tempo, depois faremos uma média dos 10 últimos valores (que em geral são todos iguais).\n",
    "\n",
    "Também, como as condições iniciais são aleatórias, se queremos saber como a velocidade depende da densidade de veículos, precisamos, para cada probabilidade, calcular várias condições iniciais e realizar médias e outras análises estatísticas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def repeat_mean_velocities(num_cells, p, num_steps, num_repetitions):\n",
    "    vel_reps = np.zeros(num_repetitions)\n",
    "    for rep in range(num_repetitions):\n",
    "        s0 = init_random(num_cells, p)\n",
    "        # Avoid having no vehicles!\n",
    "        while np.count_nonzero(s0) == 0:\n",
    "            s0 = init_random(num_cells, p)\n",
    "        states = evolve_184(s0, num_steps)\n",
    "        vel = mean_velocities(states)\n",
    "        vel_reps[rep] = np.mean(vel[-10:])\n",
    "    return vel_reps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "def evaluate_mean_velocities(num_cells, ps, num_steps, num_repetitions):\n",
    "    average_velocities = np.zeros_like(ps)\n",
    "    std_dev_velocities = np.zeros_like(ps)\n",
    "    for i, p in enumerate(ps):\n",
    "        vel_reps = repeat_mean_velocities(num_cells, p, num_steps, num_repetitions)\n",
    "        average_velocities[i] = np.mean(vel_reps)\n",
    "        std_dev_velocities[i] = np.std(vel_reps, ddof=1)\n",
    "    return average_velocities, std_dev_velocities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "ps = np.linspace(0.01, 1, 51) # 51 valores de p igualmente espaçados entre 0 e 1\n",
    "n_repetitions = 10 # Vamos fazer 10 simulações para cada valor de p\n",
    "n_cells = 400 # 200 cells\n",
    "n_steps = 100 # Number of time steps\n",
    "average_velocities, std_dev_velocities = evaluate_mean_velocities(n_cells, ps, n_steps, n_repetitions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "fig.set_size_inches(8, 6)\n",
    "ax.errorbar(ps, average_velocities, std_dev_velocities, errorevery=3)\n",
    "ax.set_xlabel('Density of cars')\n",
    "ax.set_ylabel('Average velocity');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Como vemos, para densidade de veículos abaixo de 0.5 o tráfego é livre em geral, e os carros conseguem se deslocar à velocidade máxima, mas acima dessa densidade crítica temos uma transição de fase, e o sistema passa a estar congestionado, com a velocidade média decaindo à medida que a densidade de carros aumenta."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Percolação de sítio (*site percolation*)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "No problema de percolação de sítio, partimos de uma malha com vizinhança 4. Cada ponto na malha (sítio) pode estar ou não \"ativo\", com uma probabilidade fixa $p$.\n",
    "\n",
    "Analisamos então a formação de grupos (**aglomerados** ou **clusters**) de sítios ativos ligados (conectados por vizinhança). Dizemos que ocorre *percolação* quando, no caso limite de tamanho infinito de malha, é formado um grupo de tamanho infinito.\n",
    "\n",
    "No caso de simulações que necessariamente lidam com malhas finitas, dizemos que há percolação se o tamanho do maior aglomerado cresce com o tamanho da malha.\n",
    "\n",
    "Normalmente, consideram-se condições de contorno periódicas, mas aqui, para simplificar o código, vamos considerar que não existem vizinhos no caso de células de borda."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_lattice(n, p):\n",
    "    \"\"\"Creates a 2D lattice of n x n and probability of an active site p.\"\"\"\n",
    "    lattice = (np.random.random((n,n)) < p).astype(np.int)\n",
    "    return lattice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_lattice(lattice, ax=None):\n",
    "    if ax is None:\n",
    "        fig, ax = plt.subplots()\n",
    "    ax.matshow(lattice, cmap='binary', vmin=0, vmax=1)\n",
    "    ax.set_xticks([])\n",
    "    ax.set_yticks([])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_lattice(create_lattice(20, 0.2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Precisamos agora uma função para detectar os aglomerados existentes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def detect_clusters(lattice):\n",
    "    \"\"\"Detects and returns the sizes of all the clusters of active sites in the lattice.\"\"\"\n",
    "    # We give a number for each found cluster.\n",
    "    # Find active sites\n",
    "    active_row, active_col = np.where(lattice == 1)\n",
    "    lattice_size = lattice.shape[0]\n",
    "    # First we create an array to hold the cluster number for each\n",
    "    # site. 0 means an inactive of yet unaccounted for site.\n",
    "    clusters = np.zeros_like(lattice)\n",
    "    current_cluster = 0\n",
    "    for i, j in zip(active_row, active_col):\n",
    "        cluster_neighbour_1 = clusters[i - 1,     j]\n",
    "        cluster_neighbour_2 = clusters[i    , j - 1]\n",
    "        if cluster_neighbour_1 == 0 and cluster_neighbour_2 == 0:\n",
    "            current_cluster += 1\n",
    "            clusters[i, j] = current_cluster\n",
    "        elif cluster_neighbour_1 != 0 and cluster_neighbour_2 == 0:\n",
    "            clusters[i, j] = cluster_neighbour_1\n",
    "        elif cluster_neighbour_1 == 0 and cluster_neighbour_2 != 0:\n",
    "            clusters[i, j] = cluster_neighbour_2\n",
    "        else:\n",
    "            if cluster_neighbour_2 != cluster_neighbour_1:\n",
    "                to_change = clusters == cluster_neighbour_2\n",
    "                clusters = np.where(to_change, cluster_neighbour_1, clusters)\n",
    "            clusters[i, j] = cluster_neighbour_1\n",
    "    flattend_clusters = clusters.ravel()\n",
    "    cluster_ids = flattend_clusters[np.nonzero(flattend_clusters)]\n",
    "    _, cluster_sizes = np.unique(cluster_ids, return_counts=True)\n",
    "    return cluster_sizes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "teste = create_lattice(12, 0.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_lattice(teste)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 7, 1, 3, 2, 1, 1, 3, 1, 1, 1, 1, 1, 2, 2, 1, 1, 5, 4, 1, 1, 2,\n",
       "       1], dtype=int64)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "detect_clusters(teste)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Agora queremos analisar como o tamanho dos aglomerados é afetado pela probabilidade de um site estar ativo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "def evaluate_clusters(n, p, repetitions):\n",
    "    \"\"\"Run repetitions evaluations of clusters in lattices of n x n and probability of active sites p.\"\"\"\n",
    "    all_sizes = []\n",
    "    for rep in range(repetitions):\n",
    "        lattice = create_lattice(n, p)\n",
    "        cluster_sizes_rep = detect_clusters(lattice)\n",
    "        all_sizes.append(cluster_sizes_rep)\n",
    "    return all_sizes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos avaliar como o tamanho do maior aglomerado é afetado pela probabilidade de atividade."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "lattice_size = 100\n",
    "number_of_repetitions = 20\n",
    "probabilities = np.linspace(0, 1, 21)\n",
    "max_sizes_averages = np.zeros_like(probabilities)\n",
    "max_sizes_deviations= np.zeros_like(probabilities)\n",
    "num_sites = lattice_size ** 2\n",
    "for i, p in enumerate(probabilities):\n",
    "    results_p = evaluate_clusters(lattice_size, p, number_of_repetitions)\n",
    "    max_sizes = [np.max(sizes)/num_sites if sizes.size > 0 else 0 for sizes in results_p]\n",
    "    max_sizes_averages[i] = np.mean(max_sizes)\n",
    "    max_sizes_deviations[i] = np.std(max_sizes, ddof=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "fig.set_size_inches(8, 6)\n",
    "ax.errorbar(probabilities, max_sizes_averages, max_sizes_deviations)\n",
    "ax.set_xlabel('$p$')\n",
    "ax.set_ylabel('Fraction of sites in the largest cluster');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O resultado mostra que, para $p<0.5$, o sistema se constitui de inúmeros aglomerados pequenos, mas em $p\\approx0.5$ existe uma transição de fase, e o tamanho do maior aglomerado começa a crescer com $p$, indicando que ele cresce com o número de sites ativos.\n",
    "\n",
    "Para ver melhor isso, vale a pena também plotar o resultado normalizando pelo número de sites ativos, ao invés de pelo número total de sites."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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kYKKE8XnAXcCZ7t4NLAWujLUqEZFZam3v5ogVjdRVJ4tdikjBzBji7j4I7AZOD3eNAb+PsygRkdnIZJztHT1s1qInUmGizNj2CeCvgI+Gu6qB78VZlIjIbLR19dM/Msbm1eoPl8oS5XT6HwPnAAMA7v4c0BBnUSIis/FQOKhN061KpYkS4qPu7oADmNnCeEsSEZmd1vZuFtVW0dK8qNiliBRUlBD/QTg6/SAzuwT4D+Dr8ZYlIhLd9o5ujl21mGRCK5dJZck1dzoA7v5/zex1BHOmbwQ+7u4/i70yEZEIRsbSPLqrl4tPbyl2KSIFN2OIA4ShreAWkXnnsV19pNKumdqkIs0Y4mbWR9gfnqUH2Ap82N3b4ihMRCSK1vZg5TLN1CaVKEpL/IvAc8D3CZYjvQBYATwB3AC8Mq7iRERm0treTXNDLSsX1xW7FJGCizKw7Ux3v87d+9y9192vB85y91uAJTHXJyKS00Md3WxefRBmGtQmlSdKiGfM7DwzS4S387Kem3yaXUSkYHqGUrR1DnCcZmqTChUlxP8U+DOCqVdfCB9fZGYLgCtirE1EJKffPquVy6Sy5ewTN7MkcK67v2maQ36Z/5JERKJ5KBzUtmmVQlwqU86WuLungXMLVIuIyKy0tnezrmkhi+uri12KSFFEGZ3+KzP7B+AWwvnTAdz9gdiqEhGJoLWjm1NblhW7DJGiiRLifxDeX521z4FX578cEZFonu8Z5oXeEfWHS0WLMu3qqwpRiIjIbDykSV5Eok27amZnA0cDE7MpuPvV079CRCRerR3dVCWMo1Y2FrsUkaKZ8RIzM/sacD7wPoIZ294GHBpzXSIiOW3v6ObIlY3UVSeLXYpI0US5TvwP3P3PgX3u/ingVGBNvGWJiEwvk3G2t/ewWZO8SIWLEuJD4f2gmR0CpIB18ZUkIpJbW9cAfSNjbFqt/nCpbFH6xH9qZgcBnwceIBiZ/o1YqxIRyWF85bLjNKhNKlyU0emfDh/+yMx+CtS5e0+8ZYmITK+1o5uFNUnWNy8qdikiRTVtiJvZW3I8h7vfGk9JIiK5tbZ3c+zqxSQTWrlMKluulvh086VDcEpdIS4iBTcylubRXb28+3QNzRGZNsTd/V2FLEREJIrHd/WRSjvHaVCbSKTR6SIi80Zrh2ZqExmnEBeRkvJQezdNi2pZubhu5oNFypxCXERKSmt7N8etWYyZBrWJRJl2td7M/sbMvh5ubzCzP4q/NBGRF+sdTrGjc4DN6g8XAaK1xL8FjBBMtwrQAXwmtopERKbxcEcwRYX6w0UCUUJ8vbt/jmC6Vdx9iGAhlBmZ2Zlm9oSZPWlmV01zzHlm9qiZPWJm349cuYhUnPFBbZtWa850EYg27eqomS0guDYcM1tP0DLPycySwDXA6wha7/eb2e3u/mjWMRuAjwKnufs+M1s+h59BRCpEa3s365oWclB9TbFLEZkXorTEPwH8G7DGzG4C7gY+EuF1JwFPunubu48CNwPnTjrmEuAad98H4O67I1cuIhWntb2HzWqFi0yIMnf6z8zsAeAUgtPoH3D3rgjvvQpoz9ruAE6edMzhAGb2KyAJfNLd/23yG5nZpcClAGvXro3w0SJSbkbHMjzfO6yVy0SyRL3ErA7YB/QCR5nZKyK8Zqp+c5+0XQVsAF4JXAh8I1wx7cUvcr/e3be4+5bm5uaIJYtIOekfGQM0qE0k24wtcTP7e+B84BEgE+524N4ZXtoBrMnaXg08N8Ux97l7CnjKzJ4gCPX7Zy5dRCrJwMgYVQnj6EMai12KyLwRZWDbm4GN7j7jYLZJ7gc2mNk64FngAuDtk475MUEL/Ntm1kRwer1tlp8jIhWgf2SMI1Y2UFedLHYpIvNGlNPpbUD1bN/Y3ceAK4C7gMeAH7j7I2Z2tZmdEx52F7DHzB4F7gGudPc9s/0sESlv7s7AaFqTvIhMkms98a8SnDYfBB4ys7vJurTM3d8/05u7+53AnZP2fTzrsQMfCm8iIlMaTmVIZ1z94SKT5DqdvjW83wbcPum5yQPURERiMz6o7TiFuMiL5FpP/DsAZvYBd/9y9nNm9oG4CxMRGTeUSmNAS9PCYpciMq9E6RN/xxT73pnnOkREpjWcSlNXnaQqqYUXRbLl6hO/kGA0+Tozyz6d3gBo8JmIFMxQKs0CjUoXeYlcfeL/DewCmoAvZO3vA7bHWZSIyLhUOsNIKsNSzZcu8hK5+sSfAZ5h/xKkIiIF1753EAddHy4yBXUwici8tqNzAFCIi0xFIS4i81pbZz8AC6r150pkMv1WiMi81tY5QFXCNDJdZApRFkA5DfgkcGh4vBFMttYSb2kiIrCjs18j00WmEWUBlG8CHySYuS0dbzkiIi/W1jVAXY1CXGQqUUK8x93/NfZKREQm2Tcwyt6BUdYuXVDsUkTmpSghfo+ZfR64lRcvgPJAbFWJiABtXcGgNo1MF5lalBA/ObzfkrXPgVfnvxwRkf3GLy9Tn7jI1GYMcXd/VSEKERGZrK1zgOqkUVulkekiU8k1d/pF7v49M5tyrW93/2J8ZYmIBCPTD122EDMrdiki81Kulvj4mn8NhShERGSyts5+XrZ8Ed2DqWKXIjIv5Zo7/brw/lOFK0dEJJBKZ9i5d5DXH72CB57ZV+xyROYldTSJyLzUvneQVNppaVo488EiFUohLiLzUls4Mn398kVFrkRk/lKIi8i8NH6N+PomhbjIdGYMcTP7gJk1WuCbZvaAmb2+EMWJSOXasXuAZQtrWFxfXexSROatKC3xd7t7L/B6oBl4F/B3sVYlIhWvrauf9c1qhYvkEiXExy/QPAv4lru3Zu0TEYlFW+cALc0a1CaSS5QQ32Zm/04Q4neZWQOQibcsEalk3YOj7BkYVYiLzCDK3OkXA8cBbe4+aGbLCE6pi4jEYnzO9BYNahPJKUpL3IGjgPeH2wuButgqEpGK19YZjkzX5WUiOUUJ8X8ETgUuDLf7gGtiq0hEKl5bV7DwyZolWkdcJJdIS5G6+wlm9iCAu+8zs5qY6xKRCrZjdz9rl9ZTldRUFiK5RPkNSZlZkuC0OmbWjAa2iUiM2roGdHmZSARRQvwrwL8Ay83sb4FfAp+NtSoRqVhj6QzP7BmgRSEuMqMZT6e7+01mtg14DcH14W9298dir0xEKlL7vqFg4RNdXiYyoxlD3MxudPc/Ax6fYp+ISF5NjExXS1xkRlFOpx+dvRH2j58YTzkiUukmVi9TS1xkRtOGuJl91Mz6gE1m1mtmfeH2buC2glUoIhVlR2c/SxfWcFC9LoIRmcm0Ie7un3X3BuDz7t7o7g3hbZm7f7SANYpIBWnrHFArXCSiafvEzewId38c+KGZnTD5eXd/INbKRKQitXX185ojDi52GSIlIdfAtg8BlwJfmOI5B14dS0UiUrF6BlN09WvhE5Gopg1xd780vH9V4coRkUq2o0sj00VmY8bR6Wb2tnD5UczsY2Z2q5kdH39pIlJpxkemqyUuEk2US8z+xt37zOx04A3Ad4CvxVuWiFSiHZ39VCWMNUvri12KSEmIEuLp8P5s4Fp3vw3QtR8ikndtnf0cuqyeai18IhJJlN+UZ83sOuA84E4zq434OhGRWWnr1JzpIrMRJYzPA+4CznT3bmApcGWsVYlIxRlLZ3h6z4D6w0VmIcoCKIPArVnbu4BdcRYlIpWnI1z4RCPTRaLTaXERmRfaJi4vU0tcJCqFuIjMCzt2h5eXNaklLhJVpBA3s0PN7LXh4wXj142LiORLW1c/S+qrWbJQF7+IRBVlspdLgH8Grgt3rQZ+HGdRIlJ5dnQOqD9cZJaitMQvB04DegHc/ffA8jiLEpHK09bZr5HpIrMUJcRH3H10fMPMqggWQJmRmZ1pZk+Y2ZNmdlWO495qZm5mW6K8r4iUl56h8YVPpm6J33LZqdxy2akFrkpk/osS4v9pZv8HWGBmrwN+CPxkpheZWRK4BngjcBRwoZkdNcVxDcD7gd/MpnARKR9tnVr4RGQuooT4VUAn8DBwGXAn8LEIrzsJeNLd28KW/M3AuVMc92ngc8BwpIpFpOxo4RORuZlxsheC4P2uu399lu+9CmjP2u4ATs4+IFwNbY27/9TM/nKW7y8iZWJ84ZO1WvhEZFaitMTPAX5nZjea2dlhn3gUNsW+ib50M0sAXwI+POMbmV1qZlvNbGtnZ2fEjxeRUtHWOcBaLXwiMmsz/sa4+7uAlxH0hb8d2GFm34jw3h3Amqzt1cBzWdsNwDHAL8zsaeAU4PapBre5+/XuvsXdtzQ3N0f4aBEpJW1d/ZrkRWQOIv1nr7ungH8l6NfextR925PdD2wws3VmVgNcANye9Z497t7k7oe5+2HAfcA57r51lj+DiJSwdMZ5umtQ062KzEGUyV7ONLNvA08CbwW+Aayc6XXuPgZcQbAC2mPAD9z9ETO72szOOaCqRaRsdOwbZDSd0ch0kTmI0r/9ToIW+GXuPjKbN3f3OwlGs2fv+/g0x75yNu8tIuVBI9NF5i7KUqQXFKIQEalMO8JrxKeb6EVEpjdtiJvZL939dDPr48UztBng7t4Ye3UiUvZ2dA6wpL6apVr4RGTWpg1xdz89vNeKZSISm2DOdLXCReYiysC2G6PsExGZix2dA7Q0qT9cZC6iXGJ2dPZGONnLifGUIyKVpHc4RVf/COuXqyUuMhfThriZfTTsD99kZr3hrQ94AbitYBWKSNmaGJmulrjInEwb4u7+2bA//PPu3hjeGtx9mbt/tIA1ikiZ2rFbI9NFDkSU0+n/Y2aLxzfM7CAze3OMNYlIhWjr6iephU9E5ixKiH/C3XvGN9y9G/hEfCWJSKVo6xzg0KX11FRp4RORuYjymzPVMVFXMhMRmdaOzn7N1CZyAKKE+FYz+6KZrTezFjP7EsEiKCIic5bOOE/vGVR/uMgBiBLi7wNGgVsIliMdBi6PsygRKX/P7htidCyj1ctEDkCUudMHgKsKUIuIVBDNmS5y4GYMcTNrBj5CMOlL3fh+d391jHWJSJmbCHFdIy4yZ1FOp98EPA6sAz4FPA3cH2NNIlIB2roGOEgLn4gckCghvszdvwmk3P0/3f3dwCkx1yUiZa6ts5+WpoWYWbFLESlZUUI8Fd7vMrOzzex4YHWMNYlIBdjROaD+cJEDFOV678+EM7Z9GPgq0Ah8MNaqRKSs9Q2n6OwbYb1CXOSARBmd/tPwYQ/wqnjLEZFKMLHwiS4vEzkgmutQRApufGS6rhEXOTAKcREpuLbOgXDhE4W4yIHItZ74B8L70wpXjohUgrauftZq4RORA5brN+hd4f1XC1GIiFSOHbsHNMmLSB7kGtj2mJk9DTSb2fas/Qa4u2+KtTIRKUvpjPPUngHO2Nhc7FJESt60Ie7uF5rZCuAu4JzClSQi5ey57mDhE7XERQ5czkvM3P15YLOZ1QCHh7ufcPdUjpeJiEzrSS18IpI3URZAOQP4LsGc6QasMbN3uPu9MdcmImVI14iL5E+UGdu+CLze3Z8AMLPDgX8CToyzMBEpT22d/SxeUM0yLXwicsCiXN9RPR7gAO7+O6A6vpJEpJzt6OynpVkLn4jkQ5SW+FYz+yZwY7j9p8C2+EoSkXLW1jnAH27QyHSRfIgS4u8FLgfeT9Anfi/wj3EWJSLlqW84xe6+EdYvV3+4SD5EWQBlhKBf/IvxlyMi5WxiUFuTRqaL5IPmPBSRgmnr0sInIvmkEBeRgplY+GRZfbFLESkLCnERKZgdnf2sWbKA2qpksUsRKQtRJns5HLgSODT7eHd/dYx1iUgZausc0ExtInkUZXT6D4GvAV8H0vGWIyLlKp1xnuoa4A83NBW7FJGyESXEx9z92tgrEZGy9lz3ECNjGbXERfIoSp/4T8zsL8xspZktHb/FXpmIlJUd4wufaPUykbyJ0hJ/R3h/ZdY+B1ryX46IlKvxa8TXL1dLXCRfokz2sq4QhYhIeWvr6qexrkoLn4jkUZTR6dUEU6++Itz1C+A6rSkuIrOxY3cwMl0Ln4jkT5Q+8WsJlh39x/B2YrhPRCSytq5+1mtQm0heRekTf7m7b87a/rmZtcZVkIiUn/6RMV7oHaFF062K5FWUlnjazNaPb5hZC6DreacAABCMSURBVLpeXERmoa1Tc6aLxCFKS/xK4B4zayNYivRQ4F2xViUiZWViZLpOp4vkVZTR6Xeb2QZgI0GIPx4uTyoiEklbZz8JQwufiOTZtCFuZq9295+b2VsmPbXezHD3W2OuTUTKxI7OAdYsrdfCJyJ5lqslfgbwc+BNUzzngEJcRCLZ0dmvmdpEYjBtiLv7J8KHV7v7U9nPmZkmgBGRSDLhwienv0wLn4jkW5TR6T+aYt8/57sQESlPz2rhE5HY5OoTPwI4Glg8qV+8EaiL8uZmdibwZSAJfMPd/27S8x8C/hcwBnQC73b3Z2b1E4jIvNbWFYxM1zXiIvmXq098I/BHwEG8uF+8D7hkpjc2syRwDfA6oAO438xud/dHsw57ENji7oNm9l7gc8D5s/sRRGQ+23+NuFriIvmWq0/8NuA2MzvV3X89h/c+CXjS3dsAzOxm4FxgIsTd/Z6s4+8DLprD54jIPLajs5+GuiqaFmnhE5F8i9In/h4zO2h8w8yWmNkNEV63CmjP2u4I903nYuBfp3rCzC41s61mtrWzszPCR4vIfNHWqYVPROISJcQ3uXv3+Ia77wOOj/C6qX5jfcoDzS4CtgCfn+p5d7/e3be4+5bm5uYIHy0i80Vb54CmWxWJSZQQT5jZkvENM1tKtOlaO4A1WdurgecmH2RmrwX+GjhHM8GJlJf+kTGe7x1Wf7hITKKE8ReA/zaz8cvK3gb8bYTX3Q9sCK8pfxa4AHh79gFmdjxwHXCmu++OXLWIlISnwjnTNdGLSDyizJ3+XTPbBryK4BT5WyaNMJ/udWNmdgVwF8ElZje4+yNmdjWw1d1vJzh9vgj4YdhfttPdz5n7jyMi80lbVzgyfbla4iJxiNISJwzfTsLrw81srbvvjPC6O4E7J+37eNbj186uXBEpJTt2BwufHKqFT0RiMWOfuJmdY2a/B54C/hN4mmlGkYuIZNvRNcDqJVr4RCQuUQa2fRo4Bfidu68DXgP8KtaqRKQsaGS6SLyihHjK3fcQjFJPhBO0HBdzXSJS4oKFT/o1Z7pIjKL0iXeb2SLgXuAmM9tNMNe5iMi0nusZYjiV0ZzpIjGK0hI/FxgEPgj8G7CDqdcYFxGZ0BZeXqZrxEXik7MlHi5icls4ijwDfKcgVYlIyRtf+EQtcZH45GyJu3saGDSzxQWqR0TKxI7OARpqq2heVFvsUkTKVpQ+8WHgYTP7GTAwvtPd3x9bVSJS8tq6+mlpXqiFT0RiFCXE7whvIiKRtXUOcGrLsmKXIVLWpg3x8VnZ3F394CIyKwMjY+zqGVZ/uEjMcrXEfwycAGBmP3L3PylMSSJSys6/7tcMjARXoeoacZF45RrYlt2R1RJ3ISJSPoZSaUCXl4nELVeI+zSPRURyGk6lMS18IhK7XKfTN5tZL0GLfEH4mHDb3b0x9upEpCQNpTKsXrKAumotfCISp2lD3N312yciczKcSrNptaaXEIlblGlXRUQic3eGU2lamtQfLhI3hbiI5NVoOkPGNd2qSCEoxEUkr4ZTGUAj00UKQSEuInk1NDp+eZla4iJxU4iLSF4Np9IkDJobtPCJSNwU4iKSN6l0hv6RMRZUJ7XwiUgBKMRFJC96hlK861v3MzCapknLj4oURJRVzEREcnpmzwDv/vb97Nw7SEvTQp1KFykQtcRF5ID8z1N7efM1v2LPwCg3XnyyAlykgNQSF5E5u/WBDq760cOsXrKAb77z5axr0oh0kUJSiIvIrGUyzhd/9jv+4Z4nObVlGddedAIH1dcUuyyRiqMQF5FZGU6l+fAPWrnj4V2cv2UNn37zMdRUqWdOpBgU4iIS2e6+YS757ja2d3Tzf846gkv+sEWXkokUkUJcRCJ5bFcv/+s7W9k7MMrXLjqRNxy9otgliVQ8hbiIzOjnj7/A+77/IIvqqvjhe07lmFVaZlRkPlCIi8i03J1v/eppPnPHoxx1SCPf+POXs2JxXbHLEpGQQlxEpjSWzvDJnzzC9+7byeuPOpj/d8Fx1NfoT4bIfKLfSBF5id7hFJff9AD/9fsuLjujhb96wxEkEtEGsN1y2akxVyci4xTiIvIiO/cMcvF37ueprgE+9yebOO/la4pdkohMQyEuIhO2Pr2XS2/cRjrj3HjxyZy6flmxSxKRHBTiIhXs/Ot+DQSnwH/84LN85J+3s2rJAr75ji20NC8qcnUiMhOFuEiFcw+mUP3K3b/n5HVLue7PTtQUqiIlQiEuUsEyGaeta4D/eXofbztxNX/7x8dqClWREqIQF6lAg6Nj3PN4J4/u6mVgNM1VbzyCy16hKVRFSo1CXKRCDI2mueeJ3dyxfRc/f3w3Q6k01Uljw/JFvOeM9cUuT0TmQCEuUsYmgvvhXfz8sSC4mxbV8NYTV3PWsSv50s+eUOtbpIQpxEXKzNBoml+EwX13VnD/yYmrOPvYQzhp3VKS4cQt/+8/FOAipUwhLlIGhlNBcP80PFU+OJpm2cIa3nLCKs7etJKT1y2bCG4RKR8KcZESNR7cdzz8PHc/9sJEcP/x8as4+9iVnLRuKVXJ3CPNNUWqSGlTiIuUgPFJWb7z7pP4xROd3PnwLu5+7AUGRtMsXVjDm8PgPjlCcItI+VCIi8xTI2Np2vcOsXPvAM/3DNM/MsaJn/7ZRHCfc9wq/miTglukkinERYrE3ekeTPHM3kF27h1k554BntkTPt47yPO9w7jvP74qYbxty2rOPvYQTmlRcIuIQlwkVmPpDLt6htm5dzAroPeHdd/w2IuOb26o5dCl9Zy6fhlrl9Zz6LJ61i5dyN/e8ShVCeOzb9lUpJ9EROYjhbjINDIZZyiVZmB0jKHRNIPhLXg8Fjw3Ej4eTTOYCp67Y/tzjKYzLKmvoWPfEGOZ/c3p6qSxZkk9a5fVc+KhS1i7tD4M64WsWbqA+pqpfyVv/YvTCvVji0gJUYhLyUulM2HAjgX3I/uDd2B0jMEwaAfCAJ7Yl0rzX7/rJOPOuuZFDI4Erx9KBccPpzKzqqM6aSyoTjKUSlOTTHD0qsWcdezKIKiXBUG9orFOl3qJSN7EGuJmdibwZSAJfMPd/27S87XAd4ETgT3A+e7+dJw1ZftN2x5+sLWDmiqjOpmgKpGgusqoSSaC7eSLH1cnE9RMejzdc+N/p8dnwzJgfGIsw5g8SZbZi4+d2BdumYE7ZNzJuOMO6YyH2/v3ZzJZj8f3Z6Z5nOM16YxnfR7h64LHaXc8fK+0B327E89lgufSmeC44JjwPvtxeMzE81nvN9WxD+7cR8ahpWkhA6PpIHBTQWCPpqOHbcJgYU0V9bVJ6muqGE1nSJqxeEE1KxvrqK9JsqAmycLaKhZUJ6mvSYb7qlgYPldfU7X/uJqqcF+SavVRi0iBxRbiZpYErgFeB3QA95vZ7e7+aNZhFwP73P1lZnYB8PfA+XHVNNlf/8vD7Nw7xEH11aTSGVJpZzSdIZXOvGhAkcxdwiCZMBJmJBNG0oxEwrL2QcKynk/YS1+TMMYyTgJjycIaVi3ZH6T1WeG6sDb3vvqaJLVVCU0zKiJlI86W+EnAk+7eBmBmNwPnAtkhfi7wyfDxPwP/YGbmXpgI/Y8Pv3La59IZD4M9CPfJj0fHMoyNHzOWIZXx4D6dmWgZjv8Uju9/7DD+w43/mD7xP8GxLz1uf13JRNBiD4IvCDsbf2xZj8MQNGMiDLMfJ2z/+yRt6ufGH4+/T/Z7JidqMCyxf3uq9xERkXjEGeKrgPas7Q7g5OmOcfcxM+sBlgFd2QeZ2aXApQBr166Nq94XCVqASeqqkwX5PBERkdmKsxNvqibY5BZ2lGNw9+vdfYu7b2lubs5LcSIiIqUuzhDvANZkba8GnpvuGDOrAhYDe2OsSUREpGzEGeL3AxvMbJ2Z1QAXALdPOuZ24B3h47cCPy9Uf7iIiEipi61PPOzjvgK4i+ASsxvc/REzuxrY6u63A98EbjSzJwla4BfEVY+IiEi5ifU6cXe/E7hz0r6PZz0eBt4WZw0iIiLlSrNTiIiIlCiFuIiISIlSiIuIiJQohbiIiEiJUoiLiIiUKIW4iIhIiVKIi4iIlCiFuIiISImyUpvl1Mw6gWeKXUcZaWLSqnGSF/pe80/faTz0veZfvr/TQ919ytW/Si7EJb/MbKu7byl2HeVG32v+6TuNh77X/Cvkd6rT6SIiIiVKIS4iIlKiFOJyfbELKFP6XvNP32k89L3mX8G+U/WJi4iIlCi1xEVEREqUQrxCmNmZZvaEmT1pZldN8fyHzOxRM9tuZneb2aHFqLPUzPS9Zh33VjNzM9Mo4BlE+U7N7Lzw3+sjZvb9QtdYaiL8/q81s3vM7MHwb8BZxaizlJjZDWa228x+O83zZmZfCb/z7WZ2QiyFuLtuZX4DksAOoAWoAVqBoyYd8yqgPnz8XuCWYtc9329RvtfwuAbgXuA+YEux657Pt4j/VjcADwJLwu3lxa57Pt8ifqfXA+8NHx8FPF3suuf7DXgFcALw22mePwv4V8CAU4DfxFGHWuKV4STgSXdvc/dR4Gbg3OwD3P0edx8MN+8DVhe4xlI04/ca+jTwOWC4kMWVqCjf6SXANe6+D8Dddxe4xlIT5Tt1oDF8vBh4roD1lSR3vxfYm+OQc4HveuA+4CAzW5nvOhTilWEV0J613RHum87FBP8FKbnN+L2a2fHAGnf/aSELK2FR/q0eDhxuZr8ys/vM7MyCVVeaonynnwQuMrMO4E7gfYUprazN9u/unFTl+w1lXrIp9k15WYKZXQRsAc6ItaLykPN7NbME8CXgnYUqqAxE+bdaRXBK/ZUEZ4z+y8yOcffumGsrVVG+0wuBb7v7F8zsVODG8DvNxF9e2Yr8d/dAqCVeGTqANVnbq5nidJmZvRb4a+Acdx8pUG2lbKbvtQE4BviFmT1N0C92uwa35RTl32oHcJu7p9z9KeAJglCXqUX5Ti8GfgDg7r8G6gjm/5a5i/R390ApxCvD/cAGM1tnZjXABcDt2QeEp32vIwhw9TFGk/N7dfced29y98Pc/TCCsQbnuPvW4pRbEmb8twr8mGAgJmbWRHB6va2gVZaWKN/pTuA1AGZ2JEGIdxa0yvJzO/Dn4Sj1U4Aed9+V7w/R6fQK4O5jZnYFcBfBSNUb3P0RM7sa2OrutwOfBxYBPzQzgJ3ufk7Rii4BEb9XmYWI3+ldwOvN7FEgDVzp7nuKV/X8FvE7/TDwdTP7IMEp33d6OMRapmZm/0TQpdMUjiX4BFAN4O5fIxhbcBbwJDAIvCuWOvT/k4iISGnS6XQREZESpRAXEREpUQpxERGREqUQFxERKVEKcRERkRKlEBcRESlRCnEREZESpcleRCQnM7uZYB7ow4AVwF+4+x1FLUpEALXERWRmm4E2dz8Z+FOCmalEZB7QjG0iMi0zW0Awr/Yadx82s6XAb9xdC46IzANqiYtILscAv3f34XD7BKC1iPWISBb1iYtILpuBtWZWR7B4xqeAjxS3JBEZpxAXkVw2AzcBvwAagf/P3X9V1IpEZIL6xEVkWmZ2L3CJuz9R7FpE5KUU4iIyLTN7lmBQW6bYtYjISynERURESpRGp4uIiJQohbiIiEiJUoiLiIiUKIW4iIhIiVKIi4iIlCiFuIiISIlSiIuIiJQohbiIiEiJ+v8BqQSvYUOeFjsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "fig.set_size_inches(8, 6)\n",
    "ax.errorbar(probabilities[1:], max_sizes_averages[1:]/probabilities[1:], max_sizes_deviations[1:]/probabilities[1:])\n",
    "ax.set_xlabel('$p$')\n",
    "ax.set_ylabel('Fraction of active sites in the largest cluster');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Como vemos, após a transição de fase, praticamente todos os sites ativos estão no maior aglomerado.\n",
    "\n",
    "Vejamos agora a distribuição de tamanhos de aglomerados antes, depois e durante a transição de fase."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "all_sizes = np.concatenate(evaluate_clusters(100, 0.1, 30))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "fig.set_size_inches(8, 6)\n",
    "ax.hist(all_sizes, density=True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Portanto, para $p=0.1$ há apenas aglomerados pequenos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "all_sizes = np.concatenate(evaluate_clusters(100, 0.9, 30))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "fig.set_size_inches(8, 6)\n",
    "ax.hist(all_sizes, density=True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para $p=0.6$ temos dois tipos de aglomerados: um aglomerado muito grande, com quase todos os sítios ativos, e diversos outros aglomerados muito pequenos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_loglog_histogram(values, xlabel = None, ylabel = None):\n",
    "    fig, ax = plt.subplots()\n",
    "    fig.set_size_inches(8, 6)\n",
    "    minval = np.min(values)\n",
    "    maxval = np.max(values)\n",
    "    bins = np.logspace(np.log10(minval), np.log10(maxval), 30)\n",
    "    h, _ = np.histogram(values, bins=bins)\n",
    "    ax.loglog(bins[:-1], h, 'o')\n",
    "    if xlabel:\n",
    "        ax.set_xlabel(xlabel)\n",
    "    if ylabel:\n",
    "        ax.set_ylabel(ylabel)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "all_sizes = np.concatenate(evaluate_clusters(200, 0.5, 30))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_loglog_histogram(all_sizes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Na transição, para $p=0.5$ vemos um fenômeno interessante: existem aglomerados dos mais variados tamanhos, desde muito pequenos até algumas centenas de sítios ativos.\n",
    "\n",
    "Note também no gráfico log-log que a queda é aproximadamente reta, o que indica uma distribuição da forma $P(s)\\propto s^{-\\alpha}$, onde $P(s)$ é a probabilidade de um sítio ativo qualquer estar num aglomerado de tamanho $s$. Isto é uma distribuição de **lei de potência**, ou também chamada **livre de escala**, pois esse tipo de distribuição não tem uma escala característica.\n",
    "\n",
    "Isto fica ainda mais claro se vamos mais para perto do **ponto crítico**:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "all_sizes = np.concatenate(evaluate_clusters(200, 0.59, 30))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_loglog_histogram(all_sizes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Como vemos, para $p=0.59$ a distribuição é ainda mais parecida com uma lei de potência."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Incêndio na floresta (*forest fire*)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos agora analisar um modelo simplificado da propagação de um incêndio na floresta, através de um autômato celular probabilístico.\n",
    "\n",
    "Partimos de uma malha bidimensional de células. Cada célula da malha pode estar vazia ou ser ocupada por uma árvore. A árvore pode estar normal ou pegando fogo.\n",
    "\n",
    "A cada passo, todos as árvores vizinhas a uma árvore que está pegando fogo também pegam fogo com uma probabilidade $p$. Uma árvore que pega fogo por sua vez morre e deixa a célula vazia.\n",
    "\n",
    "Inicialmente, todas as células são ocupadas por árvores e apenas a célula central está pegando fogo. O processo continua enquanto houverem árvores pegando fogo.\n",
    "\n",
    "Consideramos condições de contorno periódicas.\n",
    "\n",
    "Aqui nos interessamos por avaliar a evolução no tempo do número total de árvores queimadas e no número de árvores que estão se incendiando, além do tempo de duração do incêndio."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "def forest_fire(lattice_size, p):\n",
    "    \"\"\"Computes the dynamics of forest fire for a given latttice size and probability of spread\"\"\"\n",
    "    # Using 0: A healthy tree; 1: A burning tree; 2: Burnt tree (empty cell)\n",
    "    lattice = np.zeros((lattice_size, lattice_size), dtype=np.int)\n",
    "    lattice[lattice_size//2, lattice_size//2] = 1\n",
    "    dneighs = [(-1, 0), (0, -1), (0, 1), (1, 0)]\n",
    "    burning_trees = [(lattice_size//2, lattice_size//2)]\n",
    "    num_burning_trees = []\n",
    "    while len(burning_trees) > 0:\n",
    "        num_burning_trees.append(len(burning_trees))\n",
    "        new_burning_trees = []\n",
    "        for i, j in burning_trees:\n",
    "            for di, dj in dneighs:\n",
    "                ni = (i + di + lattice_size) % lattice_size\n",
    "                nj = (j + dj + lattice_size) % lattice_size\n",
    "                if lattice[ni, nj] == 0 and np.random.random() < p:\n",
    "                    lattice[ni, nj] = 1\n",
    "                    new_burning_trees.append((ni, nj))\n",
    "            lattice[i, j] = 2 # Mark as burnt out\n",
    "        burning_trees = new_burning_trees\n",
    "    return num_burning_trees"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "def evaluate_forest_fire(lattice_size, p, repetitions):\n",
    "    results = []\n",
    "    for rep in range(repetitions):\n",
    "        burning = forest_fire(lattice_size, p)\n",
    "        results.append(burning)\n",
    "    return results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "lattice_size = 100\n",
    "number_of_repetitions = 10\n",
    "probabilities = np.linspace(0, 1, 21)\n",
    "fire_durations = []\n",
    "burning_trees = []\n",
    "for i, p in enumerate(probabilities):\n",
    "    fires = evaluate_forest_fire(lattice_size, p, number_of_repetitions)\n",
    "    durations = [len(fire) for fire in fires]\n",
    "    fire_durations.append(durations)\n",
    "    max_durations = max(durations)\n",
    "    burning_trees_p = np.zeros((number_of_repetitions, max_durations), dtype=np.int)\n",
    "    for i, fire in enumerate(fires):\n",
    "        burning_trees_p[i] = fire + [0] * (max_durations - durations[i])\n",
    "    burning_trees.append(burning_trees_p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos ver quanto tempo os incêndios demoram em função da probabilidade de propagação."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "avg_durations = [np.mean(dur) for dur in fire_durations]\n",
    "std_durations = [np.std(dur, ddof=1) for dur in fire_durations]\n",
    "fig, ax = plt.subplots()\n",
    "fig.set_size_inches(8, 6)\n",
    "ax.errorbar(probabilities, avg_durations, std_durations);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vemos que existe uma transição brusca pouco acima de $p=0.4$: antes desse valor, o incêndio se extingue logo em seguida, após esse valor, o incêndio leva um número de passos grande (que cresce com o tamanho da malha).\n",
    "\n",
    "Agora vejamos histogramas das durações do incêndio para $p$ antes, depois e próximo ao ponto crítico.\n",
    "\n",
    "Priemiro para $p=0.1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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5KfN19An6QWfmNcKYmcaq9cD6HvXMTJhMVdVk3+PsSVxz+/a29YJrHqc+l262AgfP2j8I2DbfmCQrgEcDd/WYU5K0m/oE/TeAQ5I8NclDgJOAS+aMuQQ4tds+EfiPqhp4Ri9JWhwjX7rprrmfAXwe2AfYUFU3J3kvMFVVlwDnAv+cZAszZ/InjaPoBfS+/LMHcs3t29vWC655bOIJtiS1zW/GSlLjDHpJatweGfRJNiTZnuSmefqT5CPdoxduSHLEUtc4bkOs+bXdWm9I8pUkq5e6xnFbaM2zxv12kvuTnLhUtS2WYdac5Ogkm5LcnOS/lrK+cRvi3+tHJ/n3JNd36339Utc4bkkOTvLFJJu7Nb11wJixZtgeGfTARuDYXfSvAQ7pXmuBs5egpsW2kV2v+bvA71XVc4D30cYHWRvZ9Zp3PorjA8zcFNCCjexizUn2Bz4OvLKqngX80RLVtVg2sus/49OBb1bVauBo4IPdXX57sh3A26vqGcDzgdMHPD5mrBm2RwZ9VV3Nru/HPwE4r2ZcA+yf5IlLU93iWGjNVfWVqvpxt3sNM99r2KMN8ecM8BfAZ4Dti1/R4htiza8BLqyq73fj9+h1D7HeAvbrHp3yyG7sjqWobbFU1R1VdV23/VNgMzNPEZhtrBm2Rwb9EAY9nmHuP8iWnQZcvtxFLLYkBwKvBtYtdy1L6OnAY5L8Z5Jrk7xuuQtaZGcBz2Dmy5g3Am+tql8ub0nj0z3R97nA1+Z0jTXD+jwC4cFs6EcvtCbJi5kJ+t9d7lqWwD8A76iq+/eiZ+WtAH4LeCnwMOCrSa6pqluWt6xF83JgE/AS4GnAVUm+VFX3LG9Z/SV5JDO/jb5twHrGmmGtBv0wj2doTpLnAOcAa6rqR8tdzxKYBD7VhfxK4LgkO6rq4uUta1FtBe6sqp8BP0tyNbAaaDXoXw+8v/tG/ZYk3wV+E/j68pbVT5J9mQn5T1bVhQOGjDXDWr10cwnwuu6T6+cDd1fVHctd1GJK8mTgQuCUhs/ufkVVPbWqVlXVKmYeg/2WxkMe4LPAC5OsSPJwZp4Yu3mZa1pM32fmtxeSHAAcCty6rBX11H3ecC6wuao+NM+wsWbYHnlGn+R8Zj6BX5lkK/AeYF+AqloHXAYcB2wB7mPmrGCPNsSa383MI6A/3p3h7tjTn/w3xJqbs9Caq2pzkiuAG4BfAudU1S5vP30wG+LP+H3AxiQ3MnM54x1Vtac/uvgo4BTgxiSburZ3Ak+GxckwH4EgSY1r9dKNJKlj0EtS4wx6SWqcQS9JjTPoJalxBr0kNc6gl6TG/T+xVwWB/oQ8NAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(fire_durations[2], bins=30, density=True);\n",
    "plt.title(f'$p={probabilities[2]}$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vemos que todos os incêndios se extinguem depois de poucos passos (até 4 passos nestes resultados).\n",
    "\n",
    "Agora vejamos para $p=0.9$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(fire_durations[18], bins=30, density=True);\n",
    "plt.title(f'$p={probabilities[18]}$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Aqui vemos que todos os incêncios tomam exatamente 101 passos. Como a probabilidade de espalhamento é muito alta, o incêndio vai caminhando continuamente de uma célula para suas vizinhas, até se espalhar por toda a malha.\n",
    "\n",
    "Já próximo ao ponto crítico temos um comportamento mais interessante:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(fire_durations[10], bins=30, density=True)\n",
    "plt.title(f'$p={probabilities[10]}$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Temos incêndios que terminam rápido e indêncios de demoram muito tempo para terminar.\n",
    "\n",
    "Vejamos agora como o número de árvores queimando simultaneamente se comporta com o tempo.\n",
    "\n",
    "Primeiro, para $p=0.1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "avg_burning = [np.mean(burning, axis=0) for burning in burning_trees]\n",
    "std_burning = [np.std(burning, axis=0, ddof=1) for burning in burning_trees]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.errorbar(np.arange(avg_burning[2].size), avg_burning[2], std_burning[2]);\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('Average number of burning trees')\n",
    "plt.title(f'$p={probabilities[2]}$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vemos que o número médio de árvores queimando é sempre pequeno, e decai com o tempo. O mesmo acontece para um valor um pouco maior de $p$, mas ainda antes do ponto crítico:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.errorbar(np.arange(avg_burning[6].size), avg_burning[6], std_burning[6]);\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('Average number of burning trees')\n",
    "plt.title(f'$p={probabilities[6]}$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Já após o ponto crítico o comportamento é completamente diferente:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.errorbar(np.arange(avg_burning[18].size), avg_burning[18], std_burning[18]);\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('Average number of burning trees')\n",
    "plt.title(f'$p={probabilities[18]}$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vemos que o número de árvores queimando cresce linearmente com o tempo, até atingir um máximo, e depois vai caindo também de forma aproximadamente linear com o tempo. A queda é um efeito do tamanho finito de nossa simulação. Numa malha infinita, o número continuaria crescendo indefinidamente.\n",
    "\n",
    "Notem que quase não se notam as barras de erro neste gráfico. Isto é, existe pouca variação no comportamento.\n",
    "\n",
    "O mesmo já não ocorre próximo ao ponto crítico."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.errorbar(np.arange(avg_burning[10].size), avg_burning[10], std_burning[10], errorevery=10)\n",
    "plt.xlabel('time')\n",
    "plt.ylabel('Average number of burning trees')\n",
    "plt.title(f'$p={probabilities[10]}$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note como temos também uma subida seguida por uma descida. Mas as escalas são muito menores e as barras de erro muito maiores, o que indica grande variação entre uma simulação e outra.\n",
    "\n",
    "Vejamos agora o comportamento do número total de árvores queimadas pelos incêndios."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "burnt = [np.cumsum(burning, axis=1) for burning in burning_trees]\n",
    "avg_burnt = [np.mean(b, axis=0) for b in burnt]\n",
    "std_burnt = [np.std(b, axis=0, ddof=1) for b in burnt]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Primeiro, vejamos como ele se comporta com o tempo para $p=0.1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.errorbar(np.arange(avg_burnt[2].size), avg_burnt[2], std_burnt[2])\n",
    "plt.title(f'$p={probabilities[2]}$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notamos que o número cresce monotonicamente com o tempo, como esperado, mas sempre com valores baixos: o incêndio afeta um número pequeno de árvores.\n",
    "\n",
    "Obviamente, para $p$ grande, o número de árvores afetadas será muito maior:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.errorbar(np.arange(avg_burnt[18].size), avg_burnt[18], std_burnt[18])\n",
    "plt.title(f'$p={probabilities[18]}$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Novamente, note como não existe variação na dinâmica, demonstrada pela inexistência de barras de erro.\n",
    "\n",
    "A coisa novamente é bem diferente próximo do ponto crítico."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.errorbar(np.arange(avg_burnt[10].size), avg_burnt[10], std_burnt[10], errorevery=10)\n",
    "plt.title(f'$p={probabilities[10]}$');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vemos que não só número total de árvores atingidas é menor, como há substancial variação na dinâmica entre uma simulação e outra.\n",
    "\n",
    "Agora vejamos como a média do número total de árvores destruídas pelo incêndio se comporta com $p$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "avg_max_burnt_p = [ab[-1] for ab in avg_burnt]\n",
    "std_max_burnt_p = [sb[-1] for sb in std_burnt]\n",
    "num_trees = lattice_size * lattice_size\n",
    "plt.errorbar(probabilities, np.array(avg_max_burnt_p)/num_trees, np.array(std_max_burnt_p)/num_trees)\n",
    "plt.xlabel('$p$')\n",
    "plt.ylabel('Average fraction of tree burned');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Esta figura reforça o resultado anterior de que temos uma transição pouco depois de $p=0.4$: para valores menores, praticamente nenhuma árvore é afetada, para valores maiores, praticamente todas as árvores são afetadas."
   ]
  }
 ],
 "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
}