{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 森林火灾模拟"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "之前我们已经构建好了一些基础，但是还没有开始对火灾进行模拟。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 随机生长"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 在原来的基础上,我们要先让树生长，即定义 `grow_trees()` 方法\n",
    "- 定义方法之前，我们要先指定两个属性：\n",
    "    - 每个位置随机生长出树木的概率\n",
    "    - 每个位置随机被闪电击中的概率\n",
    "- 为了方便，我们定义一个辅助函数来生成随机 `bool` 矩阵，大小与森林大小一致\n",
    "- 按照给定的生长概率生成生长的位置，将 `trees` 中相应位置设为 `True`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "class Forest(object):\n",
    "    \"\"\" Forest can grow trees which eventually die.\"\"\"\n",
    "    def __init__(self, size=(150,150), p_sapling=0.0025, p_lightning=5.0e-6):\n",
    "        self.size = size\n",
    "        self.trees = np.zeros(self.size, dtype=bool)\n",
    "        self.fires = np.zeros((self.size), dtype=bool)\n",
    "        self.p_sapling = p_sapling\n",
    "        self.p_lightning = p_lightning\n",
    "        \n",
    "    def __repr__(self):\n",
    "        my_repr = \"{}(size={})\".format(self.__class__.__name__, self.size)\n",
    "        return my_repr\n",
    "    \n",
    "    def __str__(self):\n",
    "        return self.__class__.__name__\n",
    "    \n",
    "    @property\n",
    "    def num_cells(self):\n",
    "        \"\"\"Number of cells available for growing trees\"\"\"\n",
    "        return np.prod(self.size)\n",
    "    \n",
    "    @property\n",
    "    def tree_fraction(self):\n",
    "        \"\"\"\n",
    "        Fraction of trees\n",
    "        \"\"\"\n",
    "        num_trees = self.trees.sum()\n",
    "        return float(num_trees) / self.num_cells\n",
    "    \n",
    "    @property\n",
    "    def fire_fraction(self):\n",
    "        \"\"\"\n",
    "        Fraction of fires\n",
    "        \"\"\"\n",
    "        num_fires = self.fires.sum()\n",
    "        return float(num_fires) / self.num_cells\n",
    "    \n",
    "    def _rand_bool(self, p):\n",
    "        \"\"\"\n",
    "        Random boolean distributed according to p, less than p will be True\n",
    "        \"\"\"\n",
    "        return np.random.uniform(size=self.trees.shape) < p\n",
    "    \n",
    "    def grow_trees(self):\n",
    "        \"\"\"\n",
    "        Growing trees.\n",
    "        \"\"\"\n",
    "        growth_sites = self._rand_bool(self.p_sapling)\n",
    "        self.trees[growth_sites] = True"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "测试："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n",
      "0.00293333333333\n"
     ]
    }
   ],
   "source": [
    "forest = Forest()\n",
    "print forest.tree_fraction\n",
    "\n",
    "forest.grow_trees()\n",
    "print forest.tree_fraction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 火灾模拟"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 定义 `start_fires()`：\n",
    "    - 按照给定的概率生成被闪电击中的位置\n",
    "    - 如果闪电击中的位置有树，那么将其设为着火点\n",
    "- 定义 `burn_trees()`：\n",
    "    - 如果一棵树的上下左右有火，那么这棵树也会着火\n",
    "- 定义 `advance_one_step()`：\n",
    "    - 进行一次生长，起火，燃烧"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "class Forest(object):\n",
    "    \"\"\" Forest can grow trees which eventually die.\"\"\"\n",
    "    def __init__(self, size=(150,150), p_sapling=0.0025, p_lightning=5.0e-6):\n",
    "        self.size = size\n",
    "        self.trees = np.zeros(self.size, dtype=bool)\n",
    "        self.fires = np.zeros((self.size), dtype=bool)\n",
    "        self.p_sapling = p_sapling\n",
    "        self.p_lightning = p_lightning\n",
    "        \n",
    "    def __repr__(self):\n",
    "        my_repr = \"{}(size={})\".format(self.__class__.__name__, self.size)\n",
    "        return my_repr\n",
    "    \n",
    "    def __str__(self):\n",
    "        return self.__class__.__name__\n",
    "    \n",
    "    @property\n",
    "    def num_cells(self):\n",
    "        \"\"\"Number of cells available for growing trees\"\"\"\n",
    "        return np.prod(self.size)\n",
    "    \n",
    "    @property\n",
    "    def tree_fraction(self):\n",
    "        \"\"\"\n",
    "        Fraction of trees\n",
    "        \"\"\"\n",
    "        num_trees = self.trees.sum()\n",
    "        return float(num_trees) / self.num_cells\n",
    "    \n",
    "    @property\n",
    "    def fire_fraction(self):\n",
    "        \"\"\"\n",
    "        Fraction of fires\n",
    "        \"\"\"\n",
    "        num_fires = self.fires.sum()\n",
    "        return float(num_fires) / self.num_cells\n",
    "    \n",
    "    def _rand_bool(self, p):\n",
    "        \"\"\"\n",
    "        Random boolean distributed according to p, less than p will be True\n",
    "        \"\"\"\n",
    "        return np.random.uniform(size=self.trees.shape) < p\n",
    "    \n",
    "    def grow_trees(self):\n",
    "        \"\"\"\n",
    "        Growing trees.\n",
    "        \"\"\"\n",
    "        growth_sites = self._rand_bool(self.p_sapling)\n",
    "        self.trees[growth_sites] = True\n",
    "        \n",
    "    def start_fires(self):\n",
    "        \"\"\"\n",
    "        Start of fire.\n",
    "        \"\"\"\n",
    "        lightning_strikes = (self._rand_bool(self.p_lightning) & \n",
    "            self.trees)\n",
    "        self.fires[lightning_strikes] = True\n",
    "    \n",
    "    def burn_trees(self):\n",
    "        \"\"\"\n",
    "        Burn trees.\n",
    "        \"\"\"\n",
    "        fires = np.zeros((self.size[0] + 2, self.size[1] + 2), dtype=bool)\n",
    "        fires[1:-1, 1:-1] = self.fires\n",
    "        north = fires[:-2, 1:-1]\n",
    "        south = fires[2:, 1:-1]\n",
    "        east = fires[1:-1, :-2]\n",
    "        west = fires[1:-1, 2:]\n",
    "        new_fires = (north | south | east | west) & self.trees\n",
    "        self.trees[self.fires] = False\n",
    "        self.fires = new_fires\n",
    "        \n",
    "    def advance_one_step(self):\n",
    "        \"\"\"\n",
    "        Advance one step\n",
    "        \"\"\"\n",
    "        self.grow_trees()\n",
    "        self.start_fires()\n",
    "        self.burn_trees()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "forest = Forest()\n",
    "\n",
    "for i in range(100):\n",
    "    forest.advance_one_step()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "使用 `matshow()` 显示树木图像："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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cVNSAiN4L4GUAHp42O533PczueDztkPxaAP8PwM+HEG7K6BTva8ANg2rHuTJa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\nAz4ROBwO+ETgcDgA/H9fWFGYjphtAwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa180d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import cm\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "plt.matshow(forest.trees, cmap=cm.Greens)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "查看不同着火概率下的森林覆盖率趋势变化："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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TvdjHxwOtWikzrZejyCUOu3drYzyB1GJ/+jQPnVVryLwt5Po9jW5IrSKX2MfE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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x3ce8358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "forest = Forest()\n",
    "forest2 = Forest(p_lightning=5e-4)\n",
    "\n",
    "tree_fractions = []\n",
    "\n",
    "for i in range(2500):\n",
    "    forest.advance_one_step()\n",
    "    forest2.advance_one_step()\n",
    "    tree_fractions.append((forest.tree_fraction, forest2.tree_fraction))\n",
    "\n",
    "plt.plot(tree_fractions)\n",
    "\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}