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# Random 2D Cross-section Of (3D) Mandelbulb Fractal
# http://en.wikipedia.org/wiki/Mandelbulb
# FB - 20120707
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")

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