08.07 森林火灾模拟
森林火灾模拟
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。
随机生长
- 在原来的基础上,我们要先让树生长，即定义
grow_trees()方法 - 定义方法之前，我们要先指定两个属性：
- 每个位置随机生长出树木的概率
- 每个位置随机被闪电击中的概率
- 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 - 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
1import numpy as np
2
3class Forest(object):
4 """ Forest can grow trees which eventually die."""
5 def __init__(self, size=(150,150), p_sapling=0.0025, p_lightning=5.0e-6):
6 self.size = size
7 self.trees = np.zeros(self.size, dtype=bool)
8 self.fires = np.zeros((self.size), dtype=bool)
9 self.p_sapling = p_sapling
10 self.p_lightning = p_lightning
11
12 def __repr__(self):
13 my_repr = "{}(size={})".format(self.__class__.__name__, self.size)
14 return my_repr
15
16 def __str__(self):
17 return self.__class__.__name__
18
19 @property
20 def num_cells(self):
21 """Number of cells available for growing trees"""
22 return np.prod(self.size)
23
24 @property
25 def tree_fraction(self):
26 """
27 Fraction of trees
28 """
29 num_trees = self.trees.sum()
30 return float(num_trees) / self.num_cells
31
32 @property
33 def fire_fraction(self):
34 """
35 Fraction of fires
36 """
37 num_fires = self.fires.sum()
38 return float(num_fires) / self.num_cells
39
40 def _rand_bool(self, p):
41 """
42 Random boolean distributed according to p, less than p will be True
43 """
44 return np.random.uniform(size=self.trees.shape) < p
45
46 def grow_trees(self):
47 """
48 Growing trees.
49 """
50 growth_sites = self._rand_bool(self.p_sapling)
51 self.trees[growth_sites] = True
测试：
1forest = Forest()
2print forest.tree_fraction
3
4forest.grow_trees()
5print forest.tree_fraction
0.0
0.00293333333333
火灾模拟
- 定义
start_fires()：- 按照给定的概率生成被闪电击中的位置
- 如果闪电击中的位置有树，那么将其设为着火点
- 定义
burn_trees()：- 如果一棵树的上下左右有火，那么这棵树也会着火
- 定义
advance_one_step()：- 进行一次生长，起火，燃烧
1import numpy as np
2
3class Forest(object):
4 """ Forest can grow trees which eventually die."""
5 def __init__(self, size=(150,150), p_sapling=0.0025, p_lightning=5.0e-6):
6 self.size = size
7 self.trees = np.zeros(self.size, dtype=bool)
8 self.fires = np.zeros((self.size), dtype=bool)
9 self.p_sapling = p_sapling
10 self.p_lightning = p_lightning
11
12 def __repr__(self):
13 my_repr = "{}(size={})".format(self.__class__.__name__, self.size)
14 return my_repr
15
16 def __str__(self):
17 return self.__class__.__name__
18
19 @property
20 def num_cells(self):
21 """Number of cells available for growing trees"""
22 return np.prod(self.size)
23
24 @property
25 def tree_fraction(self):
26 """
27 Fraction of trees
28 """
29 num_trees = self.trees.sum()
30 return float(num_trees) / self.num_cells
31
32 @property
33 def fire_fraction(self):
34 """
35 Fraction of fires
36 """
37 num_fires = self.fires.sum()
38 return float(num_fires) / self.num_cells
39
40 def _rand_bool(self, p):
41 """
42 Random boolean distributed according to p, less than p will be True
43 """
44 return np.random.uniform(size=self.trees.shape) < p
45
46 def grow_trees(self):
47 """
48 Growing trees.
49 """
50 growth_sites = self._rand_bool(self.p_sapling)
51 self.trees[growth_sites] = True
52
53 def start_fires(self):
54 """
55 Start of fire.
56 """
57 lightning_strikes = (self._rand_bool(self.p_lightning) &
58 self.trees)
59 self.fires[lightning_strikes] = True
60
61 def burn_trees(self):
62 """
63 Burn trees.
64 """
65 fires = np.zeros((self.size[0] + 2, self.size[1] + 2), dtype=bool)
66 fires[1:-1, 1:-1] = self.fires
67 north = fires[:-2, 1:-1]
68 south = fires[2:, 1:-1]
69 east = fires[1:-1, :-2]
70 west = fires[1:-1, 2:]
71 new_fires = (north | south | east | west) & self.trees
72 self.trees[self.fires] = False
73 self.fires = new_fires
74
75 def advance_one_step(self):
76 """
77 Advance one step
78 """
79 self.grow_trees()
80 self.start_fires()
81 self.burn_trees()
1forest = Forest()
2
3for i in range(100):
4 forest.advance_one_step()
使用 matshow() 显示树木图像：
1import matplotlib.pyplot as plt
2from matplotlib import cm
3
4%matplotlib inline
5
6plt.matshow(forest.trees, cmap=cm.Greens)
7
8plt.show()
查看不同着火概率下的森林覆盖率趋势变化：
1forest = Forest()
2forest2 = Forest(p_lightning=5e-4)
3
4tree_fractions = []
5
6for i in range(2500):
7 forest.advance_one_step()
8 forest2.advance_one_step()
9 tree_fractions.append((forest.tree_fraction, forest2.tree_fraction))
10
11plt.plot(tree_fractions)
12
13plt.show()
