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

Koch Snowflake and Sierpinski Triangle Combination Fractal using recursion.

Python, 68 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 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68``` ```# Koch Snowflake and Sierpinski Triangle combination fractal using recursion # FB - 201003265 from PIL import Image, ImageDraw import math imgx = 512 imgy = 512 image = Image.new("L", (imgx, imgy)) draw = ImageDraw.Draw(image) def tf (x0, y0, x1, y1, x2, y2): global draw a = math.sqrt((x1 - x0) ** 2 + (y1 - y0) ** 2) b = math.sqrt((x2 - x1) ** 2 + (y2 - y1) ** 2) c = math.sqrt((x0 - x2) ** 2 + (y0 - y2) ** 2) if (a < 2) or (b < 2) or (c < 2): return x3 = (x0 + x1) / 2 y3 = (y0 + y1) / 2 x4 = (x1 + x2) / 2 y4 = (y1 + y2) / 2 x5 = (x2 + x0) / 2 y5 = (y2 + y0) / 2 draw.line ([(int(x3), int(y3)),(int(x4), int(y4))], 255) draw.line ([(int(x4), int(y4)),(int(x5), int(y5))], 255) draw.line ([(int(x5), int(y5)),(int(x3), int(y3))], 255) tf(x0, y0, x3, y3, x5, y5) tf(x3, y3, x1, y1, x4, y4) tf(x5, y5, x4, y4, x2, y2) def sf (ax, ay, bx, by): f = math.sqrt((bx - ax) ** 2 + (by - ay) ** 2) if f < 1: return f3 = f / 3 cs = (bx - ax) / f sn = (by - ay) / f cx = ax + cs * f3 cy = ay + sn * f3 h = f3 * math.sqrt(3) / 2 dx = (ax + bx) / 2 + sn * h dy = (ay + by) / 2 - cs * h ex = bx - cs * f3 ey = by - sn * f3 tf(cx, cy, dx, dy, ex, ey) sf(ax, ay, cx, cy) sf(cx, cy, dx, dy) sf(dx, dy, ex, ey) sf(ex, ey, bx, by) # main mx2 = imgx / 2 my2 = imgy / 2 r = my2 a = 2 * math.pi / 3 for k in range(3): x0 = mx2 + r * math.cos(a * k) y0 = my2 + r * math.sin(a * k) x1 = mx2 + r * math.cos(a * (k + 1)) y1 = my2 + r * math.sin(a * (k + 1)) sf(x0, y0, x1, y1) x2 = mx2 + r * math.cos(a) y2 = my2 + r * math.sin(a) tf(x0, y0, x1, y1, x2, y2) image.save("sfplustf.png", "PNG") ```
 Created by FB36 on Sat, 27 Mar 2010 (MIT)