维基百科上有个有意思的话题叫细胞自动机：https://en.wikipedia.org/wiki/Cellular_automaton
在20世纪70年代，一种名为生命游戏的二维细胞自动机变得广为人知，特别是在早期的计算机界。由约翰 · 康威发明，马丁 · 加德纳在《科学美国人》的一篇文章中推广，其规则如下：
- Any live cell with fewer than two live neighbours dies, as if caused by underpopulation.
- Any live cell with two or three live neighbours lives on to the next generation.
- Any live cell with more than three live neighbours dies, as if by overpopulation.
- Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.
总结就是：任何活细胞在有两到三个活邻居时能活到下一代，否则死亡。任何有三个活邻居的死细胞会变成活细胞，表示繁殖。
在Conway’s Game of Life中，展示了几种初始状态：
下面我们用python来模拟，首先尝试表示Beacon：
import numpy as np import matplotlib.pyplot as plt universe = np.zeros((6, 6), "byte") # Beacon universe[1:3, 1:3] = 1 universe[3:5, 3:5] = 1 print(universe) im = plt.imshow(universe, cmap="binary")
[[0 0 0 0 0 0] [0 1 1 0 0 0] [0 1 1 0 0 0] [0 0 0 1 1 0] [0 0 0 1 1 0] [0 0 0 0 0 0]]
可以看到已经成功的打印出了Beacon的形状，下面我们继续编写细胞自动机的演化规则：
def cellular_auto(universe):
universe_new = universe.copy()
h, w = universe.shape
for y in range(h):
for x in range(w):
neighbor_num = universe[x-1:x+2, y-1:y+2].sum()-universe[x, y]
# 任何有三个活邻居的死细胞都变成了活细胞，繁殖一样。
if universe[x, y] == 0 and neighbor_num == 3:
universe_new[x, y] = 1
# 任何有两到三个活邻居的活细胞都能活到下一代，否则就会死亡。
if universe[x, y] == 1 and neighbor_num not in (2, 3):
universe_new[x, y] = 0
return universe_new
universe = cellular_auto(universe)
print(universe)
plt.axis("off")
im = plt.imshow(universe, cmap="binary")
[[0 0 0 0 0 0] [0 1 1 0 0 0] [0 1 0 0 0 0] [0 0 0 0 1 0] [0 0 0 1 1 0] [0 0 0 0 0 0]]
基于此我们可以制作matplotlib的动画，下面直接将Blinker、Toad、Beacon都放上去：
from matplotlib import animation
import numpy as np
import matplotlib.pyplot as plt
%matplotlib notebook
def cellular_auto(universe):
universe_new = universe.copy()
h, w = universe.shape
for y in range(h):
for x in range(w):
neighbor_num = universe[x-1:x+2, y-1:y+2].sum()-universe[x, y]
# 任何有三个活邻居的死细胞都变成了活细胞，繁殖一样。
if universe[x, y] == 0 and neighbor_num == 3:
universe_new[x, y] = 1
# 任何有两到三个活邻居的活细胞都能活到下一代，否则就会死亡。
if universe[x, y] == 1 and neighbor_num not in (2, 3):
universe_new[x, y] = 0
return universe_new
universe = np.zeros((12, 12), "byte")
# Blinker
universe[2, 1:4] = 1
# Beacon
universe[4:6, 5:7] = 1
universe[6:8, 7:9] = 1
# Toad
universe[8, 2:5] = 1
universe[9, 1:4] = 1
fig = plt.figure()
plt.axis("off")
im = plt.imshow(universe, cmap="binary")
frame = []
for _ in range(2):
frame.append((plt.imshow(universe, cmap="binary"),))
universe = cellular_auto(universe)
animation.ArtistAnimation(fig, frame, interval=500, blit=True)
然后我们画一下Pulsar：
# Pulsar
universe = np.zeros((17, 17), "byte")
universe[[2, 7, 9, 14], 4:7] = 1
universe[[2, 7, 9, 14], 10:13] = 1
universe[4:7, [2, 7, 9, 14]] = 1
universe[10:13, [2, 7, 9, 14]] = 1
fig = plt.figure()
plt.axis("off")
im = plt.imshow(universe, cmap="binary")
frame = []
for _ in range(3):
frame.append((plt.imshow(universe, cmap="binary"),))
universe = cellular_auto(universe)
animation.ArtistAnimation(fig, frame, interval=500, blit=True)
另一种创建matplotlib动画的方法是使用FuncAnimation，完整代码：
from matplotlib import animation
import numpy as np
import matplotlib.pyplot as plt
from IPython.display import HTML
# %matplotlib notebook
def cellular_auto(universe):
universe_new = universe.copy()
h, w = universe.shape
for y in range(h):
for x in range(w):
neighbor_num = universe[x-1:x+2, y-1:y+2].sum()-universe[x, y]
# 任何有三个活邻居的死细胞都变成了活细胞，繁殖一样。
if universe[x, y] == 0 and neighbor_num == 3:
universe_new[x, y] = 1
# 任何有两到三个活邻居的活细胞都能活到下一代，否则就会死亡。
if universe[x, y] == 1 and neighbor_num not in (2, 3):
universe_new[x, y] = 0
return universe_new
def update(i=0):
global universe
im.set_data(universe)
universe = cellular_auto(universe)
return im,
# Pulsar
universe = np.zeros((17, 17), "byte")
universe[[2, 7, 9, 14], 4:7] = 1
universe[[2, 7, 9, 14], 10:13] = 1
universe[4:7, [2, 7, 9, 14]] = 1
universe[10:13, [2, 7, 9, 14]] = 1
fig = plt.figure()
plt.axis("off")
im = plt.imshow(universe, cmap="binary")
plt.show()
anim = animation.FuncAnimation(
fig, update, frames=3, interval=500, blit=True)
HTML(anim.to_jshtml())
这种动画生成速度较慢，好处是可以导出html文件：
with open("out.html", "w") as f:
f.write(anim.to_jshtml())
还可以保存MP4视频：
anim.save("out.mp4")
或gif动画：
anim.save("out.gif")
注意：保存MP4视频或GIF动画，需要事先将ffmpeg配置到环境变量中
ffmpeg下载地址：
链接: http://pan.baidu.com/s/1aioB_BwpKb6LxJs26HbbiQ?pwd=ciui
提取码: ciui
接下来，我们创建一个50*50的二维生命棋盘，并选取其中1500个位置作为初始活细胞点，我们看看最终生成的动画如何。
完整代码如下：
from matplotlib import animation
import numpy as np
import matplotlib.pyplot as plt
%matplotlib notebook
def cellular_auto(universe):
universe_new = universe.copy()
h, w = universe.shape
for y in range(1, h-1):
for x in range(1, w-1):
neighbor_num = universe[x-1:x+2, y-1:y+2].sum()-universe[x, y]
# 任何有三个活邻居的死细胞都变成了活细胞，繁殖一样。
if universe[x, y] == 0 and neighbor_num == 3:
universe_new[x, y] = 1
# 任何有两到三个活邻居的活细胞都能活到下一代，否则就会死亡。
if universe[x, y] == 1 and neighbor_num not in (2, 3):
universe_new[x, y] = 0
# 边缘置零
universe[[0, -1]] = 0
universe[:, [0, -1]] = 0
return universe_new
boardsize, pad = 50, 2
universe = np.zeros((boardsize+pad, boardsize+pad), "byte")
# 随机选取1500个点作为初始活细胞
for i in range(1500):
x, y = np.random.randint(1, boardsize+1, 2)
universe[y, x] = 1
fig = plt.figure()
plt.axis("off")
im = plt.imshow(universe, cmap="binary")
frame = []
for _ in range(200):
frame.append((plt.imshow(universe, cmap="binary"),))
universe = cellular_auto(universe)
animation.ArtistAnimation(fig, frame, interval=50, blit=True)
