A cellular automaton is a discrete model studied in computer science, mathematics, physics, complexity science, theoretical biology and microstructure modeling.
- 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.
- 当前细胞为存活状态时，当周围低于2个（不包含2个）存活细胞时， 该细胞变成死亡状态。（模拟生命数量稀少）
- 当前细胞为存活状态时，当周围有2个或3个存活细胞时， 该细胞保持原样。
- 当前细胞为存活状态时，当周围有3个以上的存活细胞时，该细胞变成死亡状态。（模拟生命数量过多）
- 当前细胞为死亡状态时，当周围有3个存活细胞时，该细胞变成存活状态。 （模拟繁殖）
Python Code 1
# Python code to implement Conway's Game Of Life
import argparse
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.animation as animation
# setting up the values for the grid
ON = 255
OFF = 0
vals = [ON, OFF]
def randomGrid(N):
"""returns a grid of NxN random values"""
return np.random.choice(vals, N * N, p=[0.2, 0.8]).reshape(N, N)
def addGlider(i, j, grid):
"""adds a glider with top left cell at (i, j)"""
glider = np.array([[0, 0, 255],
[255, 0, 255],
[0, 255, 255]])
grid[i:i + 3, j:j + 3] = glider
def addGosperGliderGun(i, j, grid):
"""adds a Gosper Glider Gun with top left
cell at (i, j)"""
gun = np.zeros(11 * 38).reshape(11, 38)
gun[5][1] = gun[5][2] = 255
gun[6][1] = gun[6][2] = 255
gun[3][13] = gun[3][14] = 255
gun[4][12] = gun[4][16] = 255
gun[5][11] = gun[5][17] = 255
gun[6][11] = gun[6][15] = gun[6][17] = gun[6][18] = 255
gun[7][11] = gun[7][17] = 255
gun[8][12] = gun[8][16] = 255
gun[9][13] = gun[9][14] = 255
gun[1][25] = 255
gun[2][23] = gun[2][25] = 255
gun[3][21] = gun[3][22] = 255
gun[4][21] = gun[4][22] = 255
gun[5][21] = gun[5][22] = 255
gun[6][23] = gun[6][25] = 255
gun[7][25] = 255
gun[3][35] = gun[3][36] = 255
gun[4][35] = gun[4][36] = 255
grid[i:i + 11, j:j + 38] = gun
def update(frameNum, img, grid, N):
# copy grid since we require 8 neighbors
# for calculation and we go line by line
newGrid = grid.copy()
for i in range(N):
for j in range(N):
# compute 8-neghbor sum
# using toroidal boundary conditions - x and y wrap around
# so that the simulaton takes place on a toroidal surface.
total = int((grid[i, (j - 1) % N] + grid[i, (j + 1) % N] +
grid[(i - 1) % N, j] + grid[(i + 1) % N, j] +
grid[(i - 1) % N, (j - 1) % N] + grid[(i - 1) % N, (j + 1) % N] +
grid[(i + 1) % N, (j - 1) % N] + grid[(i + 1) % N, (j + 1) % N]) / 255)
# apply Conway's rules
if grid[i, j] == ON:
if (total < 2) or (total > 3):
newGrid[i, j] = OFF
else:
if total == 3:
newGrid[i, j] = ON
# update data
img.set_data(newGrid)
grid[:] = newGrid[:]
return img,
# main() function
def main():
# Command line args are in sys.argv[1], sys.argv[2] ..
# sys.argv[0] is the script name itself and can be ignored
# parse arguments
parser = argparse.ArgumentParser(description="Runs Conway's Game of Life simulation.")
# add arguments
parser.add_argument('--grid-size', dest='N', required=False)
parser.add_argument('--mov-file', dest='movfile', required=False)
parser.add_argument('--interval', dest='interval', required=False)
parser.add_argument('--glider', action='store_true', required=False)
parser.add_argument('--gosper', action='store_true', required=False)
args = parser.parse_args()
# set grid size
N = 100
if args.N and int(args.N) > 8:
N = int(args.N)
# set animation update interval
updateInterval = 50
if args.interval:
updateInterval = int(args.interval)
# declare grid
grid = np.array([])
# check if "glider" demo flag is specified
if args.glider:
grid = np.zeros(N * N).reshape(N, N)
addGlider(1, 1, grid)
elif args.gosper:
grid = np.zeros(N * N).reshape(N, N)
addGosperGliderGun(10, 10, grid)
else: # populate grid with random on/off -
# more off than on
grid = randomGrid(N)
# set up animation
fig, ax = plt.subplots()
img = ax.imshow(grid, interpolation='nearest')
ani = animation.FuncAnimation(fig, update, fargs=(img, grid, N,),
frames=10,
interval=updateInterval,
save_count=50)
# # of frames?
# set output file
if args.movfile:
ani.save(args.movfile, fps=30, extra_args=['-vcodec', 'libx264'])
plt.show()
# call main
if __name__ == '__main__':
main()
Python Code 2
"""
元胞自动机 Python 实现
"""
import numpy as np
import matplotlib.pyplot as plt
class GameOfLife(object):
def __init__(self, cells_shape):
"""
Parameters
----------
cells_shape : 一个元组，表示画布的大小。
Examples
--------
建立一个高20，宽30的画布
game = GameOfLife((20, 30))
"""
# 矩阵的四周不参与运算
self.cells = np.zeros(cells_shape)
real_width = cells_shape[0] - 2
real_height = cells_shape[1] - 2
self.cells[1:-1, 1:-1] = np.random.randint(2, size=(real_width, real_height))
self.timer = 0
self.mask = np.ones(9)
self.mask[4] = 0
def update_state(self):
"""更新一次状态"""
buf = np.zeros(self.cells.shape)
cells = self.cells
for i in range(1, cells.shape[0] - 1):
for j in range(1, cells.shape[0] - 1):
# 计算该细胞周围的存活细胞数
neighbor = cells[i - 1:i + 2, j - 1:j + 2].reshape((-1,))
neighbor_num = np.convolve(self.mask, neighbor, 'valid')[0]
if neighbor_num == 3:
buf[i, j] = 1
elif neighbor_num == 2:
buf[i, j] = cells[i, j]
else:
buf[i, j] = 0
self.cells = buf
self.timer += 1
def plot_state(self):
"""画出当前的状态"""
plt.title('Iter :{}'.format(self.timer))
plt.imshow(self.cells)
plt.show()
def update_and_plot(self, n_iter):
"""更新状态并画图
Parameters
----------
n_iter : 更新的轮数
"""
plt.ion()
for _ in range(n_iter):
plt.title('Iter :{}'.format(self.timer))
plt.imshow(self.cells)
self.update_state()
plt.pause(0.2)
plt.ioff()
if __name__ == '__main__':
game = GameOfLife(cells_shape=(60, 60))
game.update_and_plot(200)