Big Hero 6

import math

import random

from PIL import Image

imgx = 512

imgy = 512

image = Image.new("RGB", (imgx, imgy))

pixels = image.load()

n = 8

# drawing area (xa < xb & ya < yb)

xa = -1.5

xb = 1.5

ya = -1.5

yb = 1.5

maxIt = 256 # max number of iterations allowed

pi2 = math.pi * 2.0

# random rotation angles to convert 2d plane to 3d plane

xy = random.random() * pi2

xz = random.random() * pi2

yz = random.random() * pi2

sxy = math.sin(xy) ; cxy = math.cos(xy)

sxz = math.sin(xz) ; cxz = math.cos(xz)

syz = math.sin(yz) ; cyz = math.cos(yz)

origx = (xa + xb) / 2.0 ; origy = (ya + yb) / 2.0

for ky in range(imgy):

    b = ky * (yb - ya) / (imgy - 1)  + ya

    for kx in range(imgx):

        a = kx * (xb - xa) / (imgx - 1)  + xa

        x = a ; y = b ; z = 0.0

        # 3d rotation around center of the plane

        x = x - origx ; y = y - origy

        x0=x*cxy-y*sxy;y=x*sxy+y*cxy;x=x0 # xy-plane rotation

        x0=x*cxz-z*sxz;z=x*sxz+z*cxz;x=x0 # xz-plane rotation 

        y0=y*cyz-z*syz;z=y*syz+z*cyz;y=y0 # yz-plane rotation

        x = x + origx ; y = y + origy

        cx = x ; cy = y ; cz = z

        for i in range(maxIt):

            r = math.sqrt(x * x + y * y + z * z)

            t = math.atan2(math.hypot(x, y), z)

            p = math.atan2(y, x)

            rn = r ** n

            x = rn * math.sin(t * n) * math.cos(p * n) + cx

            y = rn * math.sin(t * n) * math.sin(p * n) + cy

            z = rn * math.cos(t * n) + cz

            if x * x + y * y + z * z > 4.0: break

        pixels[kx, ky] = (i % 4 * 64, i % 8 * 32, i % 16 * 16)

image.save("Mandelbulb.png", "PNG")