曼德勃罗特集是人类有史以来做出的最奇异,最瑰丽的几何图形，曾被称为“上帝的指纹”。 这个点集均出自公式:Zn+1=(Zn)^{2+C，对于非线性迭代公式Zn+1=(Zn)}2+C，所有使得无限迭代后的结果能保持有限数值的复数C的集合，构成曼德勃罗集。

# /usr/bin/python
# -*- coding:utf-8 -*-

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.cm as cm


def divergent(c):
    z = 0
    i = 0
    while i < 100:
        z = z**2 + c
        if abs(z) > 2:
            break
        i += 1
    return i


def draw_mandelbrot(center_x, center_y, size):
    x1, x2 = center_x - size, center_x + size
    y1, y2 = center_y - size, center_y + size
    x, y = np.mgrid[x1:x2:500j, y1:y2:500j]
    c = x + y * 1j
    divergent_ = np.frompyfunc(divergent, 1, 1)
    mandelbrot = divergent_(c)
    mandelbrot = mandelbrot.astype(np.float64)    # ufunc返回PyObject数组
    print(size, mandelbrot.max(), mandelbrot.min())
    plt.pcolormesh(x, y, mandelbrot, cmap=cm.jet)
    plt.xlim((np.min(x), np.max(x)))
    plt.ylim((np.min(y), np.max(y)))
    plt.savefig(str(size)+'.png')
    plt.show()


if __name__ == '__main__':
    draw_mandelbrot(0, 0, 2)

    interested_x = 0.33987
    interested_y = -0.575578
    interested_x, interested_y = 0.27322626, 0.595153338
    for size in np.logspace(0, -3, 4, base=10):
        print(size)
        draw_mandelbrot(interested_x, interested_y, size)