实现Boids模型的Python代码

好的，下面是一个基本的Boids模型的Python代码：

import numpy as np
import matplotlib.pyplot as plt

# 设置模拟参数
num_boids = 50  # 粒子数
max_speed = 0.03  # 最大速度
max_force = 0.05  # 最大受力
neighborhood_radius = 0.2  # 邻域半径
separation_distance = 0.05  # 分离距离
alignment_distance = 0.1  # 对齐距离
cohesion_distance = 0.2  # 凝聚距离

# 初始化粒子位置和速度
positions = np.random.rand(num_boids, 2)
velocities = np.random.rand(num_boids, 2) * max_speed

# 模拟循环
for i in range(1000):
    # 计算邻域距离
    distances = np.sqrt(np.sum(np.square(positions[:, np.newaxis, :] - positions), axis=-1))
    neighbors = np.logical_and(distances > 0, distances < neighborhood_radius)

    # 计算三个力
    separation = np.zeros_like(positions)
    alignment = np.zeros_like(positions)
    cohesion = np.zeros_like(positions)

    for j in range(num_boids):
        # 计算分离力
        separation_vector = positions[j] - positions[neighbors[j]]
        separation_distance_mask = np.linalg.norm(separation_vector, axis=-1) < separation_distance
        separation_vector = separation_vector[separation_distance_mask]
        separation[j] = np.sum(separation_vector, axis=0)

        # 计算对齐力
        alignment_vectors = velocities[neighbors[j]]
        alignment_distance_mask = np.linalg.norm(separation_vector, axis=-1) < alignment_distance
        alignment_vectors = alignment_vectors[alignment_distance_mask]
        alignment[j] = np.sum(alignment_vectors, axis=0)

        # 计算凝聚力
        cohesion_vectors = positions[neighbors[j]]
        cohesion_distance_mask = np.linalg.norm(separation_vector, axis=-1) < cohesion_distance
        cohesion_vectors = cohesion_vectors[cohesion_distance_mask]
        cohesion[j] = np.sum(cohesion_vectors, axis=0)

    # 计算总受力
    total_force = separation + alignment + cohesion
    total_force = np.clip(total_force, -max_force, max_force)

    # 更新速度和位置
    velocities += total_force
    velocities = np.clip(velocities, -max_speed, max_speed)
    positions += velocities

    # 绘制粒子
    plt.clf()
    plt.scatter(positions[:, 0], positions[:, 1], s=5)
    plt.xlim(0, 1)
    plt.ylim(0, 1)
    plt.pause(0.01)

这段代码使用numpy和matplotlib库实现了一个简单的Boids模型，包括分离力、对齐力和凝聚力。在模拟循环中，首先计算每个粒子的邻域距离，然后根据邻域距离计算三个力，并计算总受力。最后，更新速度和位置，并绘制粒子的位置。