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748 lines
44 KiB
Markdown
748 lines
44 KiB
Markdown
# 森林火灾模拟
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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。
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## 随机生长
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* 在原来的基础上,我们要先让树生长，即定义 `grow_trees()` 方法
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* 定义方法之前，我们要先指定两个属性：
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* 每个位置随机生长出树木的概率
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* 每个位置随机被闪电击中的概率
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* 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
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* 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`
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In [1]:
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```py
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import numpy as np
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class Forest(object):
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""" Forest can grow trees which eventually die."""
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def __init__(self, size=(150,150), p_sapling=0.0025, p_lightning=5.0e-6):
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self.size = size
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self.trees = np.zeros(self.size, dtype=bool)
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self.fires = np.zeros((self.size), dtype=bool)
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self.p_sapling = p_sapling
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self.p_lightning = p_lightning
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def __repr__(self):
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my_repr = "{}(size={})".format(self.__class__.__name__, self.size)
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return my_repr
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def __str__(self):
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return self.__class__.__name__
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@property
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def num_cells(self):
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"""Number of cells available for growing trees"""
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return np.prod(self.size)
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@property
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def tree_fraction(self):
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"""
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Fraction of trees
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"""
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num_trees = self.trees.sum()
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return float(num_trees) / self.num_cells
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@property
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def fire_fraction(self):
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"""
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Fraction of fires
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"""
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num_fires = self.fires.sum()
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return float(num_fires) / self.num_cells
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def _rand_bool(self, p):
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"""
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Random boolean distributed according to p, less than p will be True
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"""
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return np.random.uniform(size=self.trees.shape) < p
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def grow_trees(self):
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"""
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Growing trees.
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"""
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growth_sites = self._rand_bool(self.p_sapling)
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self.trees[growth_sites] = True
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```
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测试：
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In [2]:
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```py
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forest = Forest()
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print forest.tree_fraction
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forest.grow_trees()
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print forest.tree_fraction
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```
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```py
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0.0
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0.00293333333333
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```
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## 火灾模拟
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* 定义 `start_fires()`：
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* 按照给定的概率生成被闪电击中的位置
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* 如果闪电击中的位置有树，那么将其设为着火点
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* 定义 `burn_trees()`：
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* 如果一棵树的上下左右有火，那么这棵树也会着火
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* 定义 `advance_one_step()`：
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* 进行一次生长，起火，燃烧
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In [3]:
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```py
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import numpy as np
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class Forest(object):
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""" Forest can grow trees which eventually die."""
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def __init__(self, size=(150,150), p_sapling=0.0025, p_lightning=5.0e-6):
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self.size = size
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self.trees = np.zeros(self.size, dtype=bool)
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self.fires = np.zeros((self.size), dtype=bool)
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self.p_sapling = p_sapling
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self.p_lightning = p_lightning
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def __repr__(self):
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my_repr = "{}(size={})".format(self.__class__.__name__, self.size)
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return my_repr
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def __str__(self):
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return self.__class__.__name__
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@property
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def num_cells(self):
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"""Number of cells available for growing trees"""
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return np.prod(self.size)
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@property
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def tree_fraction(self):
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"""
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Fraction of trees
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"""
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num_trees = self.trees.sum()
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return float(num_trees) / self.num_cells
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@property
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def fire_fraction(self):
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"""
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Fraction of fires
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"""
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num_fires = self.fires.sum()
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return float(num_fires) / self.num_cells
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def _rand_bool(self, p):
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"""
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Random boolean distributed according to p, less than p will be True
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"""
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return np.random.uniform(size=self.trees.shape) < p
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def grow_trees(self):
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"""
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Growing trees.
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"""
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growth_sites = self._rand_bool(self.p_sapling)
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self.trees[growth_sites] = True
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def start_fires(self):
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"""
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Start of fire.
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"""
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lightning_strikes = (self._rand_bool(self.p_lightning) &
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self.trees)
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self.fires[lightning_strikes] = True
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def burn_trees(self):
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"""
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Burn trees.
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"""
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fires = np.zeros((self.size[0] + 2, self.size[1] + 2), dtype=bool)
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fires[1:-1, 1:-1] = self.fires
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north = fires[:-2, 1:-1]
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south = fires[2:, 1:-1]
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east = fires[1:-1, :-2]
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west = fires[1:-1, 2:]
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new_fires = (north | south | east | west) & self.trees
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self.trees[self.fires] = False
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self.fires = new_fires
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def advance_one_step(self):
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"""
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Advance one step
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"""
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self.grow_trees()
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self.start_fires()
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self.burn_trees()
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```
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In [4]:
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```py
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forest = Forest()
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for i in range(100):
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forest.advance_one_step()
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```
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使用 `matshow()` 显示树木图像：
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In [5]:
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```py
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import matplotlib.pyplot as plt
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from matplotlib import cm
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%matplotlib inline
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plt.matshow(forest.trees, cmap=cm.Greens)
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plt.show()
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```
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查看不同着火概率下的森林覆盖率趋势变化：
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In [6]:
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```py
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forest = Forest()
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forest2 = Forest(p_lightning=5e-4)
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tree_fractions = []
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for i in range(2500):
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forest.advance_one_step()
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forest2.advance_one_step()
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tree_fractions.append((forest.tree_fraction, forest2.tree_fraction))
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plt.plot(tree_fractions)
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plt.show()
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```
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