分型圖"z=z*z+c"的畫法

python代碼：

import numpy as np
from PIL import Image
from numba import jit
MAXITERS = 200
RADIUS = 100

@jit
def color(z, i):
    v = np.log2(i+1-np.log2(np.log2(abs(z))))/5
    if v < 1.0:
        return v**4, v**2.5, v
    else:
        v = max(0, 2-v)
        return v, v**1.5, v**3

@jit
def iterate(c):
    z = 0j
    for i in range(MAXITERS):
        if z.real*z.real +z.imag*z.imag > RADIUS:
            return color(z, i)
        z = z*z + c
    return 0, 0, 0

def main(xmin, xmax, ymin, ymax, width, height):
    x = np.linspace(xmin, xmax, width)
    y = np.linspace(ymax, ymin, height)
    z = x[None, :] +y[:, None]*1j
    red, green, blue = np.asarray(np.frompyfunc(iterate, 1, 3)(z)).astype(np.float)
    img = np.dstack((red, green, blue))
    Image.fromarray(np.uint8(img*255)).save('mandelbrot.png')
    
main(-2.1, 0.8, -1.16, 1.16, 1200, 960)

效果圖：