【Python】【原创】元胞自动机与动态迁移模型

白冥 · 发表于 2025-2-3 21:00:40

概述
安装与环境配置
系列技术贴
类结构与方法
源代码
示例1-兰顿蚂蚁
示例2-草地捕食链

概述

      上一篇元胞自动机的贴子中，我们研究过森林火灾、核污染扩散，并扩展了康威的生命游戏的背景知识，这些都是动态扩散模型。众所周知，元胞自动机是一个离散动力学系统，这就说明了它不仅仅可以模拟此前我们研究过的动态扩散模型，本帖将给大家带来元胞自动机的另一种应用——动态迁移模型。
      本帖代码均由本人写就。

安装与系统配置
      本代码基于 Python 3，建议使用 Python 3.8 及以上版本。
      代码中仅使用了标准库itertools, typing，无需安装额外的第三方库。

系列技术贴
元胞自动机（一）：元胞自动机与动态扩散模型

类结构与方法
      与《元胞自动机与动态扩散模型》相同

源代码
      与《元胞自动机与动态扩散模型》相同

示例1-兰顿蚂蚁
      背景：在平面上的正方形格被填上白色。在其中一格正方形有一只“蚂蚁”。它的头部朝向上下左右其中一方。若蚂蚁在白格，右转90度，将该格改为黑格，向前移一步；若蚂蚁在黑格，左转90度，将该格改为白格，向前移一步。

if __name__ == "__main__":
from random import choice
ant_state = ["w_l", "w_r", "w_u", "w_d", "b_l", "b_r", "b_u", "b_d"]
def ant_rule(cell:Cell, neighbors:List[Cell]):
state = cell.get_state()
x, y = tuple(cell.get_coordinate())
black_neighbors = [n for n in neighbors if n.get_state() == "black"]
white_neighbors = [n for n in neighbors if n.get_state() == "white"]
ant = next([n for n in neighbors if n.get_state() in ant_state], None)
ant_moving = {
"white": {
("w_l", [x,y-1]): Cell("b_u", x, y),
("w_r", [x,y+1]): Cell("b_d", x, y),
("w_u", [x-1,y]): Cell("b_r", x, y),
("w_d", [x+1,y]): Cell("b_l", x, y),
("b_l", [x,y+1]): Cell("b_d", x, y),
("b_r", [x,y-1]): Cell("b_u", x,y),
("b_u", [x+1,y]): Cell("b_l", x,y),
("b_d", [x-1,y]): Cell("b_r", x,y)
},
"black": {
("w_l", [x,y-1]): Cell("w_u", x, y),
("w_r", [x,y+1]): Cell("w_d", x, y),
("w_u", [x-1,y]): Cell("w_r", x, y),
("w_d", [x+1,y]): Cell("w_l", x, y),
("b_l", [x,y+1]): Cell("w_d", x, y),
("b_r", [x,y-1]): Cell("w_u", x,y),
("b_u", [x+1,y]): Cell("w_l", x,y),
("b_d", [x-1,y]): Cell("w_r", x,y)
}
}
alter_color = {
"w_l": Cell("black", x, y),
"w_r": Cell("black", x, y),
"w_u": Cell("black", x, y),
"w_d": Cell("black", x, y),
"b_l": Cell("white", x, y),
"b_r": Cell("white", x, y),
"b_u": Cell("white", x, y),
"b_d": Cell("white", x, y)
}
if state in ant_moving and ant:
ant_state = ant.get_state()
ant_coord = ant.get_coordinate()
key = (ant_state, ant_coord)
if key in ant_moving[state]:
return ant_moving[state][key]
elif state in ant_state:
return alter_color[state]
return cell
def main():
L = Space()
size = (120,120)
status = ["black", "white", "w_l", "w_r", "w_u", "w_d", "b_l", "b_r", "b_u", "b_d"]
d = 2
S = Status(default = "white", *status)
N = Neighborhood(*size)
f = Rule(S, ant_rule)
ca = CA(L, d, S, N,f)
cells = []
for i in range(120):
for j in range(120):
cells.append(Cell("white", i, j))
cell = choice(cells)
towards = ["w_l", "w_r", "w_u", "w_d"]
state = choice(towards)
ant=Cell(state, *cell.get_coordinate())
cells.remove(cell)
cells.append(ant)
ca.evolution(cells, time = 100)
main()

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示例2-草地捕食链
背景：某片草地（长200，宽100）存在着羊群和狼群，羊以当地的牧草为食，狼则以羊为食。模拟草地上的形势。

全局数据结构：

sheep_state = ["s_l_str", "s_r_str", "s_u_str", "s_d_str", "s_l_lt", "s_r_lt", "s_u_lt", "s_d_lt", "s_l_rt", "s_r_rt", "s_u_rt", "s_d_rt", "s_l_sta", "s_r_sta", "s_u_sta", "s_d_sta"]
sheep_stays = ["s_l_sta", "s_r_sta", "s_u_sta", "s_d_sta"]
wolf_state = ["w_l_str", "w_r_str", "w_u_str", "w_d_str", "w_l_lt", "w_r_lt", "w_u_lt", "w_d_lt", "w_l_rt", "w_r_rt", "w_u_rt", "w_d_rt", "w_l_sta", "w_r_sta", "w_u_sta", "w_d_sta"]
wolf_stays = ["w_l_sta", "w_r_sta", "w_u_sta", "w_d_sta"]

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导入库：

from random import random
from random import choice

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代码主体：

if __name__ == "__main__":
def rule(cell:Cell, neighbors:List[Cell]):
state = cell.get_state()
x,y = tuple(cell.get_coordinate())
empty_neighbors = [n for n in neighbors if n.get_state() == "empty"]
grass_neighbors = [n for n in neighbors if n.get_state() == "grass"]
sheep_neighbors = [n for n in neighbors if n.get_state() in sheep_state]
wolf_neighbors = [n for n in neighbors if n.get_state() in wolf_state]
w_moving = {
("w_l_str", [x+1,y]): Cell("w_l_sta", x,y),
("w_r_str", [x-1,y]): Cell("w_r_sta", x,y),
("w_u_str", [x,y-1]): Cell("w_u_sta", x,y),
("w_d_str", [x,y+1]): Cell("w_d_sta", x,y),
("w_l_lt", [x+1,y+1]): Cell("w_d_sta", x,y),
("w_r_lt", [x-1,y-1]): Cell("w_u_sta", x,y),
("w_u_lt", [x+1,y-1]): Cell("w_l_sta", x,y),
("w_d_lt", [x-1,y+1]): Cell("w_r_sta", x,y),
("w_l_rt", [x+1,y-1]): Cell("w_u_sta", x,y),
("w_r_rt", [x-1,y+1]): Cell("w_d_sta", x,y),
("w_u_rt", [x-1,y-1]): Cell("w_r_sta", x,y),
("w_d_rt", [x+1,y+1]): Cell("w_l_sta", x,y)}
w_foraging = {
("w_l_sta", [x-1,y]): Cell("w_l_str", x,y),
("w_l_sta", [x-1,y-1]): Cell("w_l_lt", x,y),
("w_l_sta", [x-1,y+1]): Cell("w_l_rt",x,y),
("w_r_sta", [x+1,y]): Cell("w_r_str", x,y),
("w_r_sta", [x+1,y-1]): Cell("w_r_rt", x,y),
("w_r_sta", [x+1,y+1]): Cell("w_r_lt",x,y),
("w_u_sta", [x, y+1]): Cell("w_u_str", x,y),
("w_u_sta", [x-1, y+1]): Cell("w_u_lt", x,y),
("w_u_sta", [x+1, y+1]): Cell("w_u_rt",x,y),
("w_d_sta", [x,y-1]): Cell("w_d_str", x,y),
("w_d_sta", [x-1,y-1]): Cell("w_d_rt", x,y),
("w_d_sta", [x+1,y+1]): Cell("w_d_lt",x,y)}
s_moving = {
("s_l_str", [x+1,y]): Cell("s_l_sta", x,y),
("s_r_str", [x-1,y]): Cell("s_r_sta", x,y),
("s_u_str", [x,y-1]): Cell("s_u_sta", x,y),
("s_d_str", [x,y+1]): Cell("s_d_sta", x,y),
("s_l_lt", [x+1,y+1]): Cell("s_d_sta", x,y),
("s_r_lt", [x-1,y-1]): Cell("s_u_sta", x,y),
("s_u_lt", [x+1,y-1]): Cell("s_l_sta", x,y),
("s_d_lt", [x-1,y+1]): Cell("s_r_sta", x,y),
("s_l_rt", [x+1,y-1]): Cell("s_u_sta", x,y),
("s_r_rt", [x-1,y+1]): Cell("s_d_sta", x,y),
("s_u_rt", [x-1,y-1]): Cell("s_r_sta", x,y),
("s_d_rt", [x+1,y+1]): Cell("s_l_sta", x,y)}
s_foraging = {
("s_l_sta", [x-1,y]): Cell("s_l_str", x,y),
("s_l_sta", [x-1,y-1]): Cell("s_l_lt", x,y),
("s_l_sta", [x-1,y+1]): Cell("s_l_rt",x,y),
("s_r_sta", [x+1,y]): Cell("s_r_str", x,y),
("s_r_sta", [x+1,y-1]): Cell("s_r_rt", x,y),
("s_r_sta", [x+1,y+1]): Cell("s_r_lt",x,y),
("s_u_sta", [x, y+1]): Cell("s_u_str", x,y),
("s_u_sta", [x-1, y+1]): Cell("s_u_lt", x,y),
("s_u_sta", [x+1, y+1]): Cell("s_u_rt",x,y),
("s_d_sta", [x,y-1]): Cell("s_d_str", x,y),
("s_d_sta", [x-1,y-1]): Cell("s_d_rt", x,y),
("s_d_sta", [x+1,y+1]): Cell("s_d_lt",x,y)}
if state == "empty":
for n in wolf_neighbors:
n_state = n.get_state()
n_coord = n.get_coordinate()
if n_state in wolf_state:
if (n_state, n_coord) in w_moving:
return w_moving[(n_state, n_coord)]
for n in sheep_neighbors:
n_state = n.get_state()
n_coord = n.get_coordinate()
if n_state in sheep_state:
if (n_state, n_coord) in s_moving:
return s_moving[(n_state, n_coord)]
if len(grass_neighbors):
if random()<0.1:
return Cell("grass", x, y)
return cell
elif state == "grass":
for n in sheep_neighbors:
n_state = n.get_state()
n_coord = n.get_coordinate()
if n_state in sheep_state:
if (n_state, n_coord) in s_moving:
return s_moving[(n_state, n_coord)]
return cell
elif state in sheep_state:
if state in sheep_stays:
for n in grass_neighbors:
n_coord = n.get_coordinate()
if (state,n_coord) in s_foraging:
return s_foraging[(state,n_coord)]
elif state not in sheep_stays:
return Cell("empty", x,y)
return cell
elif state in wolf_state:
if state in wolf_stays:
for n in sheep_neighbors:
n_coord = n.get_coordinate()
if (state,n_coord) in w_foraging:
return w_foraging[(state,n_coord)]
elif state not in wolf_stays:
return Cell("empty", x,y)
return cell
def main():
L = Space()
size = (200,100)
status = ["empty", "grass", "s_l_str", "s_r_str", "s_u_str", "s_d_str", "s_l_lt", "s_r_lt", "s_u_lt", "s_d_lt", "s_l_rt", "s_r_rt", "s_u_rt", "s_d_rt", "s_l_sta", "s_r_sta", "s_u_sta", "s_d_sta", "w_l_str", "w_r_str", "w_u_str", "w_d_str", "w_l_lt", "w_r_lt", "w_u_lt", "w_d_lt", "w_l_rt", "w_r_rt", "w_u_rt", "w_d_rt", "w_l_sta", "w_r_sta", "w_u_sta", "w_d_sta"]
d = 2
S = Status(default="grass", *status)
N = Neighborhood(*size)
f = Rule(S, rule)
ca = CA(L, d, S, N,f)
cells=[]
for i in range(200):
for j in range(100):
r =random()
if r<0.6:
cells.append(Cell("grass",i,j))
elif r<0.7:
cell = Cell(choice(sheep_state),i,j)
cells.append(cell)
elif r<0.73:
cell = Cell(choice(wolf_state),i,j)
cells.append(cell)
else:
cells.append(Cell("empty",i,j))
ca.evolution(cells, time=100)
main()