ReverseGameOfLife.ipynb

{
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  "metadata": {
    "colab": {
      "name": "ReverseGameOfLife.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyPp9VymnCoFelmh1h20Q6ug",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/JoaoRibeiroMedeiros/NoiseFilters/blob/master/ReverseGameOfLife.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XTp0iO2j_8Ao",
        "colab_type": "text"
      },
      "source": [
        "#Game of Life"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "D_bspxDDUKlW",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 173
        },
        "outputId": "4b02fee9-1808-4218-8db4-488deb57c9bc"
      },
      "source": [
        "!pip install celluloid\n"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Requirement already satisfied: celluloid in /usr/local/lib/python3.6/dist-packages (0.2.0)\n",
            "Requirement already satisfied: matplotlib in /usr/local/lib/python3.6/dist-packages (from celluloid) (3.2.2)\n",
            "Requirement already satisfied: cycler>=0.10 in /usr/local/lib/python3.6/dist-packages (from matplotlib->celluloid) (0.10.0)\n",
            "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib->celluloid) (2.4.7)\n",
            "Requirement already satisfied: numpy>=1.11 in /usr/local/lib/python3.6/dist-packages (from matplotlib->celluloid) (1.18.5)\n",
            "Requirement already satisfied: kiwisolver>=1.0.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib->celluloid) (1.2.0)\n",
            "Requirement already satisfied: python-dateutil>=2.1 in /usr/local/lib/python3.6/dist-packages (from matplotlib->celluloid) (2.8.1)\n",
            "Requirement already satisfied: six in /usr/local/lib/python3.6/dist-packages (from cycler>=0.10->matplotlib->celluloid) (1.15.0)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ChdtID5fpVRE",
        "colab_type": "code",
        "colab": {
          "resources": {
            "http://localhost:8080/nbextensions/google.colab/files.js": {
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              "ok": true,
              "headers": [
                [
                  "content-type",
                  "application/javascript"
                ]
              ],
              "status": 200,
              "status_text": ""
            }
          },
          "base_uri": "https://localhost:8080/",
          "height": 72
        },
        "outputId": "29689ced-19b3-4641-b503-a103048cca36"
      },
      "source": [
        "from google.colab import files\n",
        "uploaded = files.upload()"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "\n",
              "     <input type=\"file\" id=\"files-1940ea53-89bf-4a65-a335-bc82f775cb6d\" name=\"files[]\" multiple disabled\n",
              "        style=\"border:none\" />\n",
              "     <output id=\"result-1940ea53-89bf-4a65-a335-bc82f775cb6d\">\n",
              "      Upload widget is only available when the cell has been executed in the\n",
              "      current browser session. Please rerun this cell to enable.\n",
              "      </output>\n",
              "      <script src=\"/nbextensions/google.colab/files.js\"></script> "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Saving train.csv to train.csv\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YhtgvmAbvg5U",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "w5x9zcOGJ9Mw",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from graphviz import Digraph"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lNAC7cBTg-wo",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "from celluloid import Camera\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zvl8s-g7_2cI",
        "colab_type": "text"
      },
      "source": [
        "Conway's life-step is implemented below:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Zd2S60Tyf7bk",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def evolve(lattice):\n",
        "    \"\"\"Conway's Game of life one-time evolution\"\"\"\n",
        "\n",
        "    x = np.shape(lattice)[0]\n",
        "    y = np.shape(lattice)[1]\n",
        "    latticefinal = np.copy(lattice) #without this line we have a maze generator!!!!!\n",
        "    for i in range(0,x):\n",
        "        for j in range(0,y):\n",
        "            sum = 0\n",
        "            for k in [-1,0,1]:\n",
        "                for l in [-1,0,1]:\n",
        "                    if not (k ==0 and l ==0):     \n",
        "                        sum = sum + lattice[(i+k)%x][(j+l)%y]            \n",
        "            if lattice[i][j] == 0:\n",
        "                if sum == 3: \n",
        "                    latticefinal[i][j] = 1 #reproduction \n",
        "            elif lattice[i][j] == 1:\n",
        "                if sum > 3: \n",
        "                    latticefinal[i][j] = 0 #overpopulation\n",
        "                elif sum in [2,3]: \n",
        "                    latticefinal[i][j] = 1 #stasis\n",
        "                elif sum in [0,1]: \n",
        "                    latticefinal[i][j] = 0 #underpopulation\n",
        "    return latticefinal"
      ],
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HzwdhcQRAH_m",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def evolvemap(lattice):\n",
        "    \"\"\"Conway's Game of life tracing the transition states \n",
        "    generated by the present configuration\n",
        "\n",
        "    notice: \n",
        "\n",
        "    1 - stasis\n",
        "    2 - overpopulation\n",
        "    3 - underpopulation\n",
        "    4 - reproduction\n",
        "    0 - nothingness\n",
        "    \n",
        "    \"\"\"\n",
        "    x = np.shape(lattice)[0]\n",
        "    y = np.shape(lattice)[1]\n",
        "    lattice2 = np.copy(lattice) \n",
        "    statemap = np.copy(lattice)\n",
        "    for i in range(0,x):\n",
        "        for j in range(0,y):\n",
        "            sum = 0\n",
        "            for k in [-1,0,1]:\n",
        "                for l in [-1,0,1]:\n",
        "                    if not (k ==0 and l ==0):     \n",
        "                        sum = sum + lattice[(i+k)%x][(j+l)%y]            \n",
        "            if lattice[i][j] == 0:\n",
        "                if sum == 3: \n",
        "                    lattice2[i][j] = 1 #reproduction \n",
        "                    statemap[i][j] = 4\n",
        "            elif lattice[i][j] == 1:\n",
        "                if sum > 3: \n",
        "                    lattice2[i][j] = 0 #overpopulation\n",
        "                    statemap[i][j] = 2\n",
        "                elif sum in [2,3]: \n",
        "                    lattice2[i][j] = 1 #stasis\n",
        "                    statemap[i][j] = 1\n",
        "                elif sum in [0,1]: \n",
        "                    lattice2[i][j] = 0 #underpopulation\n",
        "                    statemap[i][j] = 3\n",
        "    return lattice2, statemap"
      ],
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "99gheS_lUWLA",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def generate_lattice(n,p):\n",
        "    lattice = np.zeros([n,n], dtype='int')\n",
        "    for i in range(0,n):\n",
        "        for j in range(0,n):\n",
        "            if np.random.uniform() < p:\n",
        "                lattice[i,j]=1\n",
        "    return lattice\n",
        "\n",
        "def generate_lattice_s(n,m,p):\n",
        "    lattice = np.zeros([n,m], dtype='int')\n",
        "    for i in range(0,n):\n",
        "        for j in range(0,m):\n",
        "            if np.random.uniform() < p:\n",
        "                lattice[i,j]=1\n",
        "    return lattice\n",
        "\n",
        "def generate_lattice_pq(n,p,q):\n",
        "    lattice = np.zeros([n,n], dtype='int')\n",
        "    for i in range(0,n):\n",
        "        for j in range(0,n):\n",
        "            if i > p and i < q and j > p and j < q:\n",
        "                lattice[i,j]=1\n",
        "    return lattice\n",
        "\n",
        "def generate_lattice_pq_s(n,m,p,q):\n",
        "    lattice = np.zeros([n,m], dtype='int')\n",
        "    for i in range(0,n):\n",
        "        for j in range(0,m):\n",
        "            if i > p and i < q and j > p and j < q:\n",
        "                lattice[i,j]=1\n",
        "    return lattice"
      ],
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AGz7s98HgQwy",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#X =  generate_lattice_pq(31,11,15)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "avJIVEN_HQRM",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "X =  generate_lattice_pq_s(25,20,7,15) #kaggle shape\n",
        "X0 =  generate_lattice_s(25,20,0.5) #kaggle shape"
      ],
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "F81VbvErb0lA",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "t = np.zeros((25,20))\n",
        "for i in range(25):\n",
        "  for j in range(20):\n",
        "    t[i,j] = i+j*20\n"
      ],
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DI3N0WOXcaIv",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "19aac34f-7d73-4d20-97c7-76b027399ac3"
      },
      "source": [
        "plt.imshow(t)"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7fc00b12a390>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 15
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BwHBUFC_ds4U",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "4241b754-91ab-4fac-ec97-346ef27131fa"
      },
      "source": [
        "plt.imshow(X)"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7fc00b124908>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAANAAAAD4CAYAAACdW2gvAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAJEElEQVR4nO3dTYhdBxmH8edvm6ZYFVpaQ2yLigQhG0cZqmCRSv1Iu0ndiF1IFoXpwoKCm+BGl91oV6WQ0tAstCJqaRbFWoNQBBGjBE39oKVUTEwTSwW7qm19XcwJTNNMZnLfO3Pusc8Phns+7sx5ufBwz5x7Z26qCkmzedfYA0hTZkBSgwFJDQYkNRiQ1HDldh7squysq7lmOw8ptb3Kv16uqhsutm9bA7qaa/hkbt/OQ0ptv6gf/229fa1TuCT7kvw1yfNJDnZ+ljRFMweU5ArgQeAOYC9wd5K98xpMmoLOM9AtwPNV9UJV/Qf4IbB/PmNJ09AJ6Ebg72vWTw3b3iLJSpLjSY6/zmuNw0mLZ8svY1fVoaparqrlHezc6sNJ26oT0Gng5jXrNw3bpHeMTkC/BfYk+XCSq4CvAEfnM5Y0DTO/DlRVbyS5D3gKuAI4XFXPzm0yaQJaL6RW1ZPAk3OaRZoc3wsnNRiQ1GBAUoMBSQ0GJDUYkNRgQFKDAUkNBiQ1GJDUYEBSgwFJDQYkNRiQ1GBAUoMBSQ0GJDUYkNRgQFKDAUkNBiQ1GJDUYEBSgwFJDQYkNRiQ1GBAUoMBSQ0GJDUYkNRgQFKDAUkNBiQ1GJDU0PqIxyQvAq8CbwJvVNXyPIaSpqIV0OCzVfXyHH6ONDmewkkN3YAK+HmS3yVZudgdkqwkOZ7k+Ou81jyctFi6p3C3VtXpJO8Hnk7yl6p6Zu0dquoQcAjgfbmumseTFkrrGaiqTg+354DHgVvmMZQ0FTMHlOSaJO89vwx8ATg5r8GkKeicwu0CHk9y/uf8oKp+NpeppImYOaCqegH42BxnkSbHy9hSgwFJDQYkNRiQ1GBAUoMBSQ0GJDUYkNRgQFKDAUkNBiQ1GJDUYEBSgwFJDQYkNRiQ1DCP/wunpqf+cWLsEbbVFz+wNPYIc+MzkNRgQFKDAUkNBiQ1GJDUYEBSgwFJDQYkNRiQ1GBAUoMBSQ0GJDUYkNRgQFKDAUkNBiQ1GJDUYEBSw4YBJTmc5FySk2u2XZfk6STPDbfXbu2Y0mLazDPQo8C+C7YdBI5V1R7g2LAuveNsGFBVPQO8csHm/cCRYfkIcNec55ImYdb/yrOrqs4Myy8Bu9a7Y5IVYAXgat494+GkxdS+iFBVBdQl9h+qquWqWt7Bzu7hpIUya0Bnk+wGGG7PzW8kaTpmDegocGBYPgA8MZ9xpGnZzGXsx4BfAx9NcirJPcD9wOeTPAd8bliX3nE2vIhQVXevs+v2Oc8iTY7vRJAaDEhqMCCpwYCkBgOSGgxIajAgqcGApAYDkhoMSGowIKnBgKQGA5IaDEhqMCCpwYCkBgOSGgxIajAgqcGApAYDkhoMSGowIKnBgKQGA5IaDEhqMCCpwYCkBgOSGgxIajAgqcGApAYDkhpm/Zh7zdEXP7A09gia0WY+I/VwknNJTq7Z9p0kp5OcGL7u3NoxpcW0mVO4R4F9F9n+QFUtDV9PzncsaRo2DKiqngFe2YZZpMnpXES4L8kfhlO8a9e7U5KVJMeTHH+d1xqHkxbPrAE9BHwEWALOAN9d745VdaiqlqtqeQc7ZzyctJhmCqiqzlbVm1X1X+Bh4Jb5jiVNw0wBJdm9ZvVLwMn17iv9P9vwdaAkjwG3AdcnOQV8G7gtyRJQwIvAvVs4o7SwNgyoqu6+yOZHtmAWaXJ8K4/UYEBSgwFJDQYkNRiQ1GBAUoMBSQ0GJDUYkNRgQFKDAUkNBiQ1GJDUYEBSgwFJDQYkNRiQ1GBAUoMBSQ0GJDUYkNRgQFKDAUkNBiQ1GJDUYEBSgwFJDQYkNRiQ1GBAUoMBSQ0GJDUYkNRgQFKDAUkNGwaU5OYkv0zypyTPJvn6sP26JE8neW64vXbrx5UWy2aegd4AvllVe4FPAV9Lshc4CByrqj3AsWFdekfZMKCqOlNVvx+WXwX+DNwI7AeODHc7Aty1VUNKi2rDj7lfK8mHgI8DvwF2VdWZYddLwK51vmcFWAG4mnfPOqe0kDZ9ESHJe4CfAN+oqn+v3VdVBdTFvq+qDlXVclUt72Bna1hp0WwqoCQ7WI3n+1X102Hz2SS7h/27gXNbM6K0uDZzFS7AI8Cfq+p7a3YdBQ4MyweAJ+Y/nrTYNvM70KeBrwJ/THJi2PYt4H7gR0nuAf4GfHlrRpQW14YBVdWvgKyz+/b5jiNNi+9EkBoMSGowIKnBgKQGA5IaDEhqMCCpwYCkBgOSGgxIajAgqcGApAYDkhoMSGowIKnBgKQGA5IaDEhqMCCpwYCkBgOSGgxIajAgqcGApAYDkhoMSGowIKnBgKQGA5IaDEhqMCCpwYCkBgOSGrL6AdvbdLDkn6x+HOR51wMvb9sAfVOad0qzwmLP+8GquuFiO7Y1oLcdPDleVcujDXCZpjTvlGaF6c17nqdwUoMBSQ1jB3Ro5ONfrinNO6VZYXrzAiP/DiRN3djPQNKkGZDUMFpASfYl+WuS55McHGuOzUjyYpI/JjmR5PjY81woyeEk55KcXLPtuiRPJ3luuL12zBnXWmfe7yQ5PTzGJ5LcOeaMmzVKQEmuAB4E7gD2Ancn2TvGLJfhs1W1tKCvVTwK7Ltg20HgWFXtAY4N64viUd4+L8ADw2O8VFVPbvNMMxnrGegW4PmqeqGq/gP8ENg/0iyTV1XPAK9csHk/cGRYPgLcta1DXcI6807SWAHdCPx9zfqpYduiKuDnSX6XZGXsYTZpV1WdGZZfAnaNOcwm3ZfkD8Mp3sKccl6KFxE259aq+gSrp5xfS/KZsQe6HLX6WsWiv17xEPARYAk4A3x33HE2Z6yATgM3r1m/adi2kKrq9HB7Dnic1VPQRXc2yW6A4fbcyPNcUlWdrao3q+q/wMNM4zEeLaDfAnuSfDjJVcBXgKMjzXJJSa5J8t7zy8AXgJOX/q6FcBQ4MCwfAJ4YcZYNnY998CWm8Rhz5RgHrao3ktwHPAVcARyuqmfHmGUTdgGPJ4HVx+sHVfWzcUd6qySPAbcB1yc5BXwbuB/4UZJ7WP0Tki+PN+FbrTPvbUmWWD3VfBG4d7QBL4Nv5ZEavIggNRiQ1GBAUoMBSQ0GJDUYkNRgQFLD/wBT7/Sc/yks9wAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qt1T4X0Y5IVD",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "608e78ef-d377-4ab2-d2d1-01023b48e8ee"
      },
      "source": [
        "plt.imshow(evolve(X))"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7fc00b079a20>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "B4qx2ZEYP0Hq",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "lattice2, statemap = evolvemap(X)"
      ],
      "execution_count": 22,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "v-UgDPrtSlOB",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "lattice2, statemap = evolvemap(X)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "D3GCxWSTSLpy",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "872583c1-d5d3-4486-a648-7032124a7ac2"
      },
      "source": [
        "plt.imshow(statemap)"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7fc00afa84a8>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 23
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fCsEt6POdusQ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 267
        },
        "outputId": "91792bd1-39bb-4b2f-f55e-2f7393cefafc"
      },
      "source": [
        "Y =  generate_lattice(50,0.5)\n",
        "fig = plt.figure()\n",
        "camera = Camera(fig)\n",
        "for i in range(1,100):\n",
        "    plt.imshow( Y, cmap = 'magma')\n",
        "    Y =  evolve(Y)\n",
        "    camera.snap()\n",
        "animation = camera.animate()\n",
        "animation.save('gameoflife3.gif', writer = 'pillow')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HMzQwLQw6KXC",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 17
        },
        "outputId": "962d2b21-75aa-47fa-eb62-81f62f128772"
      },
      "source": [
        "from google.colab import files\n",
        "files.download( \"gameoflife3.gif\" )    "
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "\n",
              "    async function download(id, filename, size) {\n",
              "      if (!google.colab.kernel.accessAllowed) {\n",
              "        return;\n",
              "      }\n",
              "      const div = document.createElement('div');\n",
              "      const label = document.createElement('label');\n",
              "      label.textContent = `Downloading \"${filename}\": `;\n",
              "      div.appendChild(label);\n",
              "      const progress = document.createElement('progress');\n",
              "      progress.max = size;\n",
              "      div.appendChild(progress);\n",
              "      document.body.appendChild(div);\n",
              "\n",
              "      const buffers = [];\n",
              "      let downloaded = 0;\n",
              "\n",
              "      const channel = await google.colab.kernel.comms.open(id);\n",
              "      // Send a message to notify the kernel that we're ready.\n",
              "      channel.send({})\n",
              "\n",
              "      for await (const message of channel.messages) {\n",
              "        // Send a message to notify the kernel that we're ready.\n",
              "        channel.send({})\n",
              "        if (message.buffers) {\n",
              "          for (const buffer of message.buffers) {\n",
              "            buffers.push(buffer);\n",
              "            downloaded += buffer.byteLength;\n",
              "            progress.value = downloaded;\n",
              "          }\n",
              "        }\n",
              "      }\n",
              "      const blob = new Blob(buffers, {type: 'application/binary'});\n",
              "      const a = document.createElement('a');\n",
              "      a.href = window.URL.createObjectURL(blob);\n",
              "      a.download = filename;\n",
              "      div.appendChild(a);\n",
              "      a.click();\n",
              "      div.remove();\n",
              "    }\n",
              "  "
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "application/javascript": [
              "download(\"download_d68142ea-defa-4c00-b119-887fa18e21b7\", \"gameoflife3.gif\", 1463806)"
            ],
            "text/plain": [
              "<IPython.core.display.Javascript object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OjoKTVAkDPmS",
        "colab_type": "text"
      },
      "source": [
        "#Viterbi Approach\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ewUgiRlgSVky",
        "colab_type": "text"
      },
      "source": [
        "Let's say the hidden states are the origins of a specific state in the lattice, i.e. the transitions that produce an observable present, namely state the four conway rules :\n",
        "\n",
        "* Stasis = $S$\n",
        "* Overpopulation = $O$\n",
        "* Underpopulation = $U$\n",
        "* Reproduction = $R$\n",
        "\n",
        "Notice the transitions associated with each hidden state, and the fifth transition $Z$:\n",
        "\n",
        "* $S :\\, 1 \\rightarrow 1$\n",
        "* $O :\\, 1 \\rightarrow 0$\n",
        "* $U :\\, 1 \\rightarrow 0$ \n",
        "* $R :\\, 0 \\rightarrow 1$\n",
        "* $Z :\\, 0 \\rightarrow 0$\n",
        "\n",
        "\n",
        "Let's define the sets  of $3 \\, \\times \\, 3$ matrixes associated with each hidden state.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YR55w9__lzzB",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "matrices = []\n",
        "for a1 in [0,1]:\n",
        "  for a2 in [0,1]:\n",
        "    for a3 in [0,1]:\n",
        "      for a4 in [0,1]:\n",
        "        for a5 in [0,1]:\n",
        "          for a6 in [0,1]:\n",
        "            for a7 in [0,1]:\n",
        "              for a8 in [0,1]:\n",
        "                for a9 in [0,1]:\n",
        "                  matrices.append(np.array([[a1, a2, a3],[a4, a5, a6],[a7, a8, a9]]))\n",
        "      \n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CET6U6-Qnjlo",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "53bbed7e-9a6e-465b-e053-282a34c5feec"
      },
      "source": [
        "matrices[230]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[[0, 1, 1], [1, 0, 0], [1, 1, 0]]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0exUM4-zw8sY",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "matrixs = {}"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FyWu_XoEnNv5",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "b0d397d6-a1cb-4a75-90e6-95259d41f203"
      },
      "source": [
        "np.sum(matrices[230])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "5"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fnP4towPlbt8",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "matrizS = []\n",
        "matrizO = []\n",
        "matrizU = []\n",
        "matrizR = []\n",
        "matrizZ = []\n",
        "\n",
        "for i in matrices:\n",
        "  if i[1][1] == 1:\n",
        "    if (np.sum(i)-1) in [2,3]:\n",
        "      matrizS.append(i)\n",
        "    if (np.sum(i)-1) in [0,1]:\n",
        "      matrizU.append(i)\n",
        "    if (np.sum(i)-1) > 3:\n",
        "      matrizO.append(i)\n",
        "  if i[1][1] == 0:\n",
        "    if np.sum(i) == 3:\n",
        "      matrizR.append(i)\n",
        "    else: matrizZ.append(i)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oQ80WrkXLNU4",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 119
        },
        "outputId": "e5c7ffdd-728c-4bc9-bbac-0a13d361b843"
      },
      "source": [
        "print(len(matrices))\n",
        "print(len(matrizS))\n",
        "print(len(matrizO))\n",
        "print(len(matrizU))\n",
        "print(len(matrizR))\n",
        "print(len(matrizZ))\n",
        "\n",
        "matriz = [matrizZ,matrizS,matrizO,matrizU,matrizR]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "512\n",
            "84\n",
            "163\n",
            "9\n",
            "56\n",
            "200\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "h33JN-DY_DFu",
        "colab_type": "text"
      },
      "source": [
        "For implementing viterbi we must write the emission matrix and the transition matrix!"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2SNPU6V_UQsM",
        "colab_type": "text"
      },
      "source": [
        "##Transition Matrix "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AGRgi_yCXsam",
        "colab_type": "text"
      },
      "source": [
        "Transition matrix will measure the probability of transitions between hidden states!\n",
        "\n",
        " 1 - stasis - $S$\n",
        "\n",
        " 2 - overpopulation - $O$\n",
        "\n",
        " 3 - underpopulation - $U$\n",
        "\n",
        " 4 - reproduction - $R$\n",
        "\n",
        " 0 - nothingness - $Z$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "64ITTTaiMdQQ",
        "colab_type": "text"
      },
      "source": [
        "First we'll do using the abstract states, then the $3 \\times 3$ matrix configurations associated with each state"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MgVEQVRGkyA7",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#state dictionary\n",
        "\n",
        "SD = {'S','O', 'U','R','Z' }"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SeQjXbVrac2D",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "#TM = {'S|S':0, 'O|S':0, 'U|S':0, 'R|O':0, 'Z|O':0, 'R|U':0, 'Z|U':0,\n",
        "#      'U|R':0, 'O|R':0, 'S|R':0, 'R|Z':0, 'Z|Z':0 }\n",
        "TM = {'S':{'S':0, 'O':0 , 'U':0}, 'O':{'R':0, 'Z':0},'U':{'R':0, 'Z':0},\n",
        "      'R':{'S':0, 'O':0 , 'U':0}, 'Z':{'R':0,'Z':0}}\n",
        "TMa = {}"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CriQla1xWGLP",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "d-zIpg_Y3NwV",
        "colab_type": "text"
      },
      "source": [
        "##Emission Matrix"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SkOWNWk33Ste",
        "colab_type": "text"
      },
      "source": [
        "Emission matrix will carry the probabilities of observing the living (1) or dead state (0) given the 5 hidden states"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "R17CVen65b8W",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "EM = {'S': {0:0, 1:1}, 'O':{0:0, 1:1},'U':{0:0, 1:1},\n",
        "      'R':{0:1, 1:0}, 'Z':{0:1, 1:0}}\n",
        "EMa = {}"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rf1XgDqHVI_4",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "Y = np.copy(X0)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MjZTvB07jBkm",
        "colab_type": "text"
      },
      "source": [
        "temporal transition!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XuOdm_7V_Ck8",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "Y, statemap0 = evolvemap(Y)\n",
        "x = np.shape(Y)[0]\n",
        "y = np.shape(Y)[1]\n",
        "for i in range(0,1000):\n",
        "  Y, statemap = evolvemap(Y)\n",
        "  for j in range(x):\n",
        "    for l in range(y):\n",
        "      if statemap0[j][l]==1 and statemap[j][l]==1: TM['S']['S'] +=1\n",
        "      if statemap0[j][l]==1 and statemap[j][l]==2: TM['S']['O'] +=1\n",
        "      if statemap0[j][l]==1 and statemap[j][l]==3: TM['S']['U'] +=1\n",
        "      if statemap0[j][l]==2 and statemap[j][l]==4: TM['O']['R'] +=1\n",
        "      if statemap0[j][l]==2 and statemap[j][l]==0: TM['O']['Z'] +=1\n",
        "      if statemap0[j][l]==3 and statemap[j][l]==4: TM['U']['R'] +=1\n",
        "      if statemap0[j][l]==3 and statemap[j][l]==0: TM['U']['Z'] +=1\n",
        "      if statemap0[j][l]==4 and statemap[j][l]==1: TM['R']['S'] +=1\n",
        "      if statemap0[j][l]==4 and statemap[j][l]==2: TM['R']['O'] +=1\n",
        "      if statemap0[j][l]==4 and statemap[j][l]==3: TM['S']['S'] +=1\n",
        "      if statemap0[j][l]==0 and statemap[j][l]==4: TM['Z']['R'] +=1\n",
        "      if statemap0[j][l]==0 and statemap[j][l]==0: TM['Z']['Z'] +=1\n",
        "  statemap0 = np.copy(statemap)\n",
        "  \n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JMHM5-y9jDyu",
        "colab_type": "text"
      },
      "source": [
        "spacial transition!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "G0QHmV5bjHIr",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "Y, statemap0 = evolvemap(Y)\n",
        "x = np.shape(Y)[0]\n",
        "y = np.shape(Y)[1]\n",
        "for i in listadeY:\n",
        "  for j in range(x):\n",
        "    for l in range(y):\n",
        "      if statemap0[j][l]==1 and statemap[j][l+1]==1: TM['S']['S'] +=1\n",
        "      if statemap0[j][l]==1 and statemap[j][l]==2: TM['S']['O'] +=1\n",
        "      if statemap0[j][l]==1 and statemap[j][l]==3: TM['S']['U'] +=1\n",
        "      if statemap0[j][l]==2 and statemap[j][l]==4: TM['O']['R'] +=1\n",
        "      if statemap0[j][l]==2 and statemap[j][l]==0: TM['O']['Z'] +=1\n",
        "      if statemap0[j][l]==3 and statemap[j][l]==4: TM['U']['R'] +=1\n",
        "      if statemap0[j][l]==3 and statemap[j][l]==0: TM['U']['Z'] +=1\n",
        "      if statemap0[j][l]==4 and statemap[j][l]==1: TM['R']['S'] +=1\n",
        "      if statemap0[j][l]==4 and statemap[j][l]==2: TM['R']['O'] +=1\n",
        "      if statemap0[j][l]==4 and statemap[j][l]==3: TM['S']['S'] +=1\n",
        "      if statemap0[j][l]==0 and statemap[j][l]==4: TM['Z']['R'] +=1\n",
        "      if statemap0[j][l]==0 and statemap[j][l]==0: TM['Z']['Z'] +=1\n",
        "  statemap0 = np.copy(statemap)\n",
        "  "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LQZq49NMjSUp",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "Y = evolve(Y)\n",
        "x = np.shape(Y)[0]\n",
        "y = np.shape(Y)[1]\n",
        "for n in range(0,1000):\n",
        "  Y, statemap0 = evolvemap(Y)\n",
        "  for i in range(x):\n",
        "    for j in range(y):\n",
        "      for k in [0,1,2,3,4]:\n",
        "        for l in matriz[k]:\n",
        "          if np.all(Y[i-1:i+2,j-1:j+2]==l):\n",
        "            TMa = {}\n",
        "\n",
        "      \n",
        "  statemap0 = np.copy(statemap)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xAsoWNaYj9zH",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "d56111e8-b8fb-4c0f-9cab-da785e12105d"
      },
      "source": [
        "np.all(Y[0:3,1:4] == matrizZ[0])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "True"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wODv_Uyc2YRl",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "S=[0,1,2,3,4]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YQteHKLEBv-I",
        "colab_type": "text"
      },
      "source": [
        "##Viterbi algorithm\n",
        "\n",
        "implementing Viterbi algorithm\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mvc-ABiwkLwF",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def viterbi(O,S,P,Y,TM,EM):\n",
        "  \"\"\" viterbi algithm\n",
        "  O - > espaço de observação - [0,1] ou 3x3\n",
        "  S - > espaço de estados - [SOURZ] ou 3x3\n",
        "  P - > probabilidade do estado inicial\n",
        "  Y - > sequencia de observacoes\n",
        "  TM - > matriz de transicoes (A)\n",
        "  EM - > matriz de emissoes (B)\n",
        "  \"\"\"\n",
        "  \n",
        "  for s in S:\n",
        "    T1[s,1] = P[s][] * EM[s][y1]\n",
        "    T2[s,1] = 0\n",
        "  \n",
        "  for j in Y: #comeca na segunda observação T é o tamanho de Y\n",
        "    for s in S:\n",
        "      T1[s,j] = max(k) ( T1[k,j-1]* TM[k][i] * EM[s][j])\n",
        "      T2[s,j] = argmax(k) ( T1[k,j-1]* TM[k][i] * EM[s][j])\n",
        "\n",
        "  x[T] = argmax(k) (T1[k,T]) \n",
        " \n",
        "  # agora na ordem inversa\n",
        "\n",
        "  for j in reverse(Y):\n",
        "    x[j-1] = argmax(k) (T2[x[j],j])\n",
        "  \n",
        "  return x"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NdXDsvWRvpUb",
        "colab_type": "text"
      },
      "source": [
        "#visualizing training set"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KlIPg3noxLxI",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import pandas as pd"
      ],
      "execution_count": 26,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Aq25rG08jtTZ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "df = pd.read_csv('train.csv')"
      ],
      "execution_count": 28,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9FjUyRZm1011",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "6cabfb4d-b811-48a3-a49f-adbbdfa8c2c9"
      },
      "source": [
        "np.shape(df)"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(50000, 1252)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TKaRg6RVxX32",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "a0c2fc81-117a-4275-ceaa-e817b53c0316"
      },
      "source": [
        "df['delta'].unique()"
      ],
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([3, 4, 5, 1, 2])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "A7nh9RcfMG8x",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "listastart = ['start_' + str(i) for i in range(0,625)]\n",
        "listastop = ['stop_' + str(i) for i in range(0,625)]"
      ],
      "execution_count": 45,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YcerTFsOTBn8",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "starts = df[listastart]\n",
        "stops = df[listastop]"
      ],
      "execution_count": 46,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ERoCizL5aOmw",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "16722efc-f30a-4744-f664-2cc5c705b221"
      },
      "source": [
        "starts['start_0'][0]"
      ],
      "execution_count": 59,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 59
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HjA-y366TOe5",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "startssquare = []\n",
        "for i in range(50000):\n",
        "  x = np.zeros((25,25))\n",
        "  for j in range(25):\n",
        "    for k in range(25):\n",
        "      x[j][k] = starts['start_'+ str(j*25 + k)][i]\n",
        "  startssquare.append(x)\n"
      ],
      "execution_count": 61,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "msjtZinFgQ1D",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "stopssquare = []\n",
        "for i in range(50000):\n",
        "  x = np.zeros((25,25))\n",
        "  for j in range(25):\n",
        "    for k in range(25):\n",
        "      x[j][k] = stops['stop_'+ str(j*25 + k)][i]\n",
        "  stopssquare.append(x)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EhjcTRCxgDl9",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "outputId": "624b1581-c2bb-492a-fe77-7d23cd95a7a7"
      },
      "source": [
        "plt.imshow(startssquare[3])"
      ],
      "execution_count": 65,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.image.AxesImage at 0x7fc008845550>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 65
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kyAy9SLGTSZa",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 253
        },
        "outputId": "4acd1e3d-a8ef-4060-862a-16683db4a38c"
      },
      "source": [
        "df.head()"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>id</th>\n",
              "      <th>delta</th>\n",
              "      <th>start_0</th>\n",
              "      <th>start_1</th>\n",
              "      <th>start_2</th>\n",
              "      <th>start_3</th>\n",
              "      <th>start_4</th>\n",
              "      <th>start_5</th>\n",
              "      <th>start_6</th>\n",
              "      <th>start_7</th>\n",
              "      <th>start_8</th>\n",
              "      <th>start_9</th>\n",
              "      <th>start_10</th>\n",
              "      <th>start_11</th>\n",
              "      <th>start_12</th>\n",
              "      <th>start_13</th>\n",
              "      <th>start_14</th>\n",
              "      <th>start_15</th>\n",
              "      <th>start_16</th>\n",
              "      <th>start_17</th>\n",
              "      <th>start_18</th>\n",
              "      <th>start_19</th>\n",
              "      <th>start_20</th>\n",
              "      <th>start_21</th>\n",
              "      <th>start_22</th>\n",
              "      <th>start_23</th>\n",
              "      <th>start_24</th>\n",
              "      <th>start_25</th>\n",
              "      <th>start_26</th>\n",
              "      <th>start_27</th>\n",
              "      <th>start_28</th>\n",
              "      <th>start_29</th>\n",
              "      <th>start_30</th>\n",
              "      <th>start_31</th>\n",
              "      <th>start_32</th>\n",
              "      <th>start_33</th>\n",
              "      <th>start_34</th>\n",
              "      <th>start_35</th>\n",
              "      <th>start_36</th>\n",
              "      <th>start_37</th>\n",
              "      <th>...</th>\n",
              "      <th>stop_585</th>\n",
              "      <th>stop_586</th>\n",
              "      <th>stop_587</th>\n",
              "      <th>stop_588</th>\n",
              "      <th>stop_589</th>\n",
              "      <th>stop_590</th>\n",
              "      <th>stop_591</th>\n",
              "      <th>stop_592</th>\n",
              "      <th>stop_593</th>\n",
              "      <th>stop_594</th>\n",
              "      <th>stop_595</th>\n",
              "      <th>stop_596</th>\n",
              "      <th>stop_597</th>\n",
              "      <th>stop_598</th>\n",
              "      <th>stop_599</th>\n",
              "      <th>stop_600</th>\n",
              "      <th>stop_601</th>\n",
              "      <th>stop_602</th>\n",
              "      <th>stop_603</th>\n",
              "      <th>stop_604</th>\n",
              "      <th>stop_605</th>\n",
              "      <th>stop_606</th>\n",
              "      <th>stop_607</th>\n",
              "      <th>stop_608</th>\n",
              "      <th>stop_609</th>\n",
              "      <th>stop_610</th>\n",
              "      <th>stop_611</th>\n",
              "      <th>stop_612</th>\n",
              "      <th>stop_613</th>\n",
              "      <th>stop_614</th>\n",
              "      <th>stop_615</th>\n",
              "      <th>stop_616</th>\n",
              "      <th>stop_617</th>\n",
              "      <th>stop_618</th>\n",
              "      <th>stop_619</th>\n",
              "      <th>stop_620</th>\n",
              "      <th>stop_621</th>\n",
              "      <th>stop_622</th>\n",
              "      <th>stop_623</th>\n",
              "      <th>stop_624</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>2</td>\n",
              "      <td>3</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>3</td>\n",
              "      <td>5</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>4</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>...</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>5 rows × 1252 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "   id  delta  start_0  start_1  ...  stop_621  stop_622  stop_623  stop_624\n",
              "0   0      3        0        0  ...         0         0         0         0\n",
              "1   1      4        0        0  ...         0         0         0         0\n",
              "2   2      3        0        1  ...         0         0         0         0\n",
              "3   3      5        0        1  ...         0         0         1         0\n",
              "4   4      1        0        0  ...         0         0         0         0\n",
              "\n",
              "[5 rows x 1252 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 42
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LXPx6exA4ZR5",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 248
        },
        "outputId": "8dc916db-2fbc-45d0-ab78-debd9155187a"
      },
      "source": [
        "import networkx as nx\n",
        "\n",
        "G = nx.DiGraph()\n",
        "G.add_node('S')\n",
        "G.add_node('O')\n",
        "G.add_node('U')\n",
        "G.add_node('R')\n",
        "G.add_node('Z')\n",
        "G.add_edge('S','S')\n",
        "G.add_edge('S','O')\n",
        "G.add_edge('S','U')\n",
        "G.add_edge('O','R')\n",
        "G.add_edge('O','Z')\n",
        "G.add_edge('U','R')\n",
        "G.add_edge('U','Z')\n",
        "G.add_edge('R','S')\n",
        "G.add_edge('R','O')\n",
        "G.add_edge('R','U')\n",
        "G.add_edge('Z','R')\n",
        "G.add_edge('Z','Z')\n",
        "#G.add_edges_from()\n",
        "nx.draw_networkx(G, pos=nx.circular_layout(G) ,arrowsize=20)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3uE-5-uAJ2Rp",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from networkx.drawing.nx_agraph import write_dot"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KrqOD1-5gWMN",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 464
        },
        "outputId": "c5242ade-d6de-4c52-a2be-87d9fac26145"
      },
      "source": [
        "import networkx as nx\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "G = Digraph('G')\n",
        "G.edge('S','S')\n",
        "G.edge('S','O')\n",
        "G.edge('S','U')\n",
        "G.edge('O','R')\n",
        "G.edge('O','Z')\n",
        "G.edge('U','R')\n",
        "G.edge('U','Z')\n",
        "G.edge('R','S')\n",
        "G.edge('R','O')\n",
        "G.edge('R','U')\n",
        "G.edge('Z','R')\n",
        "G.edge('Z','Z')\n",
        "G"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<graphviz.dot.Digraph at 0x7f41f193f9e8>"
            ],
            "image/svg+xml": "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n<!-- Generated by graphviz version 2.40.1 (20161225.0304)\n -->\n<!-- Title: G Pages: 1 -->\n<svg width=\"130pt\" height=\"332pt\"\n viewBox=\"0.00 0.00 130.28 332.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 328)\">\n<title>G</title>\n<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-328 126.28,-328 126.28,4 -4,4\"/>\n<!-- S -->\n<g id=\"node1\" class=\"node\">\n<title>S</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"39.28\" cy=\"-306\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"39.28\" y=\"-302.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">S</text>\n</g>\n<!-- S&#45;&gt;S -->\n<g id=\"edge1\" class=\"edge\">\n<title>S&#45;&gt;S</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M59.175,-318.4321C71.968,-321.6753 84.28,-317.5313 84.28,-306 84.28,-297.6218 77.7806,-293.1433 69.3195,-292.5644\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"68.7819,-289.1004 59.175,-293.5679 69.471,-296.0665 68.7819,-289.1004\"/>\n</g>\n<!-- O -->\n<g id=\"node2\" class=\"node\">\n<title>O</title>\n<ellipse fill=\"none\" stroke=\"#000000\" cx=\"39.28\" cy=\"-234\" rx=\"27\" ry=\"18\"/>\n<text text-anchor=\"middle\" x=\"39.28\" y=\"-230.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">O</text>\n</g>\n<!-- S&#45;&gt;O -->\n<g id=\"edge2\" class=\"edge\">\n<title>S&#45;&gt;O</title>\n<path fill=\"none\" stroke=\"#000000\" d=\"M39.28,-287.8314C39.28,-280.131 39.28,-270.9743 39.28,-262.4166\"/>\n<polygon fill=\"#000000\" stroke=\"#000000\" points=\"42.7801,-262.4132 39.28,-252.4133 35.7801,-262.4133 42.7801,-262.4132\"/>\n</g>\n<!-- U -->\n<g id=\"node3\" 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          },
          "metadata": {
            "tags": []
          },
          "execution_count": 70
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XKOC0GoX6PoA",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qy38rKMxWCCx",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "center = {}\n",
        "neighbours = {}\n",
        "\n",
        "\n",
        "center['S'] = 1\n",
        "neighbours['S'] = [[1,1,0,0,0,0,0,0],\n",
        "                  [1,1,1,0,0,0,0,0]]\n",
        "\n",
        "center['O'] = 1\n",
        "neighbours['O'] = [[1,1,1,1,0,0,0,0]\n",
        "              ,[1,1,1,1,1,0,0,0]\n",
        "              ,[1,1,1,1,1,1,0,0]\n",
        "              ,[1,1,1,1,1,1,1,0]\n",
        "              ,[1,1,1,1,1,1,1,1]]\n",
        "\n",
        "center['U'] = 1\n",
        "neighbours['U'] = [[0,0,0,0,0,0,0,0]\n",
        "              ,[1,0,0,0,0,0,0,0]]\n",
        "\n",
        "center['R'] = 0\n",
        "neighbours['R'] = [[1,1,1,0,0,0,0,0]]\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}