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]]
ArtistAnimation动画
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)
FuncAnimation动画
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: https://pan.baidu.com/s/1aioB_BwpKb6LxJs26HbbiQ?pwd=ciui
提取码: ciui
随机生命游戏
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)
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