曼德勃罗python

曼德勃罗集是一种分形图形，可以用迭代的方式生成。下面是一个简单的Python实现：

import matplotlib.pyplot as plt
import numpy as np

def mandelbrot(c, max_iter):
    z = c
    n = 0
    while abs(z) <= 2 and n < max_iter:
        z = z*z + c
        n += 1
    if n == max_iter:
        return 0
    else:
        return n

def mandelbrot_set(xmin, xmax, ymin, ymax, width, height, max_iter):
    x, y = np.meshgrid(np.linspace(xmin, xmax, width), np.linspace(ymin, ymax, height))
    c = x + y*1j
    mandelbrot_set = np.zeros((height, width))
    for i in range(height):
        for j in range(width):
            mandelbrot_set[i,j] = mandelbrot(c[i,j], max_iter)
    return mandelbrot_set

mandelbrot = mandelbrot_set(-2, 1, -1, 1, 1000, 1000, 100)
plt.imshow(mandelbrot, cmap='hot', extent=(-2, 1, -1, 1))
plt.show()

这个实现使用了numpy和matplotlib库。函数`mandelbrot`计算给定复数`c`的曼德勃罗迭代次数，函数`mandelbrot_set`生成曼德勃罗集。最后，我们使用`imshow`函数将曼德勃罗集可视化。