Welcome, guest | Sign In | My Account | Store | Cart

It draws a random 2D cross-section of Mandelbulb fractal.

Python, 51 lines
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51``` ```# 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") ```
 Created by FB36 on Sun, 8 Jul 2012 (MIT)