元胞自动机 食物链模型

### 元胞自动机实现食物链模型算法示例 元胞自动机是一种离散的动力学系统，通过简单的局部规则来模拟复杂的行为模式。在生态系统的建模中，特别是食物链的研究方面，元胞自动机可以用来描述物种之间的相互作用。 #### 定义网格和状态 在一个二维矩形网格上定义不同类型的细胞，每种细胞代表生态系统中的一个实体： - **空白格子 (0)**：表示没有任何生物存在的区域。 - **植物 (1)**：作为初级生产者，提供能量源。 - **食草动物 (2)**：依赖于植物生存。 - **食肉动物 (3)**：捕猎食草动物以获取能量。 ```python import numpy as np from matplotlib import pyplot as plt import random # 初始化参数设置 grid_size = 50 num_steps = 100 initial_plants_density = 0.4 initial_herbivores_density = 0.1 initial_carnivores_density = 0.05 def initialize_grid(grid_size, initial_densities): grid = np.zeros((grid_size, grid_size), dtype=int) # 设置初始密度分布 for i in range(grid_size): for j in range(grid_size): r = random.random() if r < initial_densities['plants']: grid[i][j] = 1 elif r < initial_densities['herbivores'] + initial_densities['plants']: grid[i][j] = 2 elif r < sum(initial_densities.values()): grid[i][j] = 3 return grid # 更新函数 def update_cell(state, neighbors): new_state = state plant_neighbors = sum([n==1 for n in neighbors]) herbivore_neighbors = sum([n==2 for n in neighbors]) carnivore_neighbors = sum([n==3 for n in neighbors]) if state == 0 and plant_neighbors >= 2: new_state = 1 # 新生植物 elif state == 1 and herbivore_neighbors > 0: new_state = 0 # 被吃掉的植物 elif state == 2 and carnivore_neighbors > 0: new_state = 0 # 食草动物被捕杀 elif state == 2 and plant_neighbors >= 1: new_state = 2 # 生存并繁殖 elif state == 3 and herbivore_neighbors >= 1: new_state = 3 # 生存并繁殖 return new_state # 主循环更新整个网格的状态 for step in range(num_steps): next_grid = np.copy(current_grid) for x in range(grid_size): for y in range(grid_size): current_state = current_grid[x,y] neighbor_positions = [(x+i, y+j) % grid_size for i in (-1,0,1) for j in (-1,0,1)] neighbor_states = [current_grid[pos] for pos in neighbor_positions] updated_state = update_cell(current_state, neighbor_states) next_grid[x,y] = updated_state current_grid = next_grid plt.imshow(current_grid, cmap='viridis') plt.show() ``` 这段代码展示了如何创建一个基本的食物链模型，在这个例子中只考虑了三种主要成分——植物、食草动物以及食肉动物，并且简单地实现了它们之间基于邻域关系的变化逻辑[^1]。