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維基百科上有個有意思的話題叫細胞自動機：https://en.wikipedia.org/wiki/Cellular_automaton

在20世紀70年代，一種名為生命游戲的二維細胞自動機變得廣為人知，特別是在早期的計算機界。由約翰 · 康威發明，馬丁 · 加德納在《科學美國人》的一篇文章中推廣，其規則如下：

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.

總結就是：任何活細胞在有兩到三個活鄰居時能活到下一代，否則死亡。任何有三個活鄰居的死細胞會變成活細胞，表示繁殖。

在Conway’s Game of Life中，展示了幾種初始狀態：

下面我們用python來模擬，首先嘗試表示Beacon：

import numpy as np import matplotlib.pyplot as pltuniverse = 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]]

可以看到已經成功的打印出了Beacon的形狀，下面我們繼續編寫細胞自動機的演化規則：

def cellular_auto(universe):universe_new = universe.copy()h, w = universe.shapefor y in range(h):for x in range(w):neighbor_num = universe[x-1:x+2, y-1:y+2].sum()-universe[x, y]# 任何有三個活鄰居的死細胞都變成了活細胞，繁殖一樣。if universe[x, y] == 0 and neighbor_num == 3:universe_new[x, y] = 1# 任何有兩到三個活鄰居的活細胞都能活到下一代，否則就會死亡。if universe[x, y] == 1 and neighbor_num not in (2, 3):universe_new[x, y] = 0return universe_newuniverse = 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動畫

基于此我們可以制作matplotlib的動畫，下面直接將Blinker、Toad、Beacon都放上去：

from matplotlib import animation import numpy as np import matplotlib.pyplot as plt %matplotlib notebookdef cellular_auto(universe):universe_new = universe.copy()h, w = universe.shapefor y in range(h):for x in range(w):neighbor_num = universe[x-1:x+2, y-1:y+2].sum()-universe[x, y]# 任何有三個活鄰居的死細胞都變成了活細胞，繁殖一樣。if universe[x, y] == 0 and neighbor_num == 3:universe_new[x, y] = 1# 任何有兩到三個活鄰居的活細胞都能活到下一代，否則就會死亡。if universe[x, y] == 1 and neighbor_num not in (2, 3):universe_new[x, y] = 0return universe_newuniverse = 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)

然后我們畫一下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動畫

另一種創建matplotlib動畫的方法是使用FuncAnimation，完整代碼：

from matplotlib import animation import numpy as np import matplotlib.pyplot as plt from IPython.display import HTML # %matplotlib notebookdef cellular_auto(universe):universe_new = universe.copy()h, w = universe.shapefor y in range(h):for x in range(w):neighbor_num = universe[x-1:x+2, y-1:y+2].sum()-universe[x, y]# 任何有三個活鄰居的死細胞都變成了活細胞，繁殖一樣。if universe[x, y] == 0 and neighbor_num == 3:universe_new[x, y] = 1# 任何有兩到三個活鄰居的活細胞都能活到下一代，否則就會死亡。if universe[x, y] == 1 and neighbor_num not in (2, 3):universe_new[x, y] = 0return universe_newdef update(i=0):global universeim.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())

這種動畫生成速度較慢，好處是可以導出html文件：

with open("out.html", "w") as f:f.write(anim.to_jshtml())

還可以保存MP4視頻：

anim.save("out.mp4")

或gif動畫：

anim.save("out.gif")

注意：保存MP4視頻或GIF動畫，需要事先將ffmpeg配置到環境變量中

ffmpeg下載地址：https://pan.baidu.com/s/1Cfu198zvz57BCy5yR4e0qA?pwd=a729

隨機生命游戲

接下來，我們創建一個50*50的二維生命棋盤，并選取其中1500個位置作為初始活細胞點，我們看看最終生成的動畫如何。

完整代碼如下：

from matplotlib import animation import numpy as np import matplotlib.pyplot as plt %matplotlib notebookdef cellular_auto(universe):universe_new = universe.copy()h, w = universe.shapefor 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]# 任何有三個活鄰居的死細胞都變成了活細胞，繁殖一樣。if universe[x, y] == 0 and neighbor_num == 3:universe_new[x, y] = 1# 任何有兩到三個活鄰居的活細胞都能活到下一代，否則就會死亡。if universe[x, y] == 1 and neighbor_num not in (2, 3):universe_new[x, y] = 0# 邊緣置零universe[[0, -1]] = 0universe[:, [0, -1]] = 0return universe_newboardsize, pad = 50, 2 universe = np.zeros((boardsize+pad, boardsize+pad), "byte") # 隨機選取1500個點作為初始活細胞 for i in range(1500):x, y = np.random.randint(1, boardsize+1, 2)universe[y, x] = 1fig = 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)

總結

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