from PIL import Image,ImageColor
import math, cmath

def compact(z):
    return str(round(50-50*math.exp(-4*(math.pow(abs(z),2)))))

def deg(x):
    return int(math.degrees(x)+180)

def Transform(z):
    try:
        W=cmath.log(z)
        return ImageColor.getrgb("hsl("+str(deg(cmath.phase(W)))+",100%,"+compact(W)+"%)")
    except ValueError:
        return ImageColor.getrgb("hsl(0,100%,100%)")

A=1000
B=1000
I_min=-10
I_max=10
R_min=-10
R_max=10

def main():

    size = width, hieght = A,B;

    im=Image.new("RGB",size)

    for x in range(A):
        for y in range(B):
            im.putpixel((x,y),Transform(complex((x-A/2)/(A/2)*(R_max-R_min)/2,(y-B/2)/(B/2)*(I_max-I_min)/2)))

    im.show()
    im.save("ln(z).png")
    del im

if __name__ == '__main__':
    main()