正十二面体万花筒

转自：http://www.sohu.com/a/134487713_505803

代码：

'''
A kaleidoscope pattern with icosahedral symmetry.
'''
import numpy as np
from PIL import Image
from matplotlib.colors import hsv_to_rgb
def Klein(z):
    '''Klein's j-function'''
    return 1728*(z *(z**10+11*z**5-1))**5/(-(z**20+1) +228*(z**15-z**5) -494*z**10)**3
def RiemannSphere(z):
    '''
    map the complex plane to Riemann's sphere via stereographic projection
    '''
    t = 1+z.real*z.real +z.imag*z.imag
    return 2*z.real/t, 2*z.imag/t, 2/t-1
def Mobius(z):
    '''
    distort the result image by a mobius transformation
    '''
    return(z -20)/(3*z +1j)
def main(imgsize):
    x = np.linspace(-6, 6, imgsize)
    y = np.linspace(6, -6, imgsize)
    z = x[None, :] +y[:, None]*1j
    z = RiemannSphere(Klein(Mobius(Klein(z))))
    #define colors in hsv space
    H = np.sin(z[0]*np.pi)**2
    S = np.cos(z[1]*np.pi)**2
    V = abs(np.sin(z[2]*np.pi) *np.cos(z[2]*np.pi))**0.2
    HSV = np.dstack((H, S, V))
    #transform to rgb space
    img =hsv_to_rgb(HSV)
    Image.fromarray(np.uint8(img*255)).save('kaleidoscope.png')

import time
start =time.time()
main(imgsize=800)
end = time.time()
print('runtime: {:3f}seconds'.format(end - start))

运行结果：