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Regular Polygon IFS Fractals (Python recipe) by FB36
ActiveState Code (http://code.activestate.com/recipes/577115/)

5 Regular Polygon IFS Fractals.

Python, 29 lines
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# Regular Polygon IFS Fractal
# FB - 201003151
from PIL import Image
import math
import random
# image size
imgx = 512
imgy = 512

for n in range(3, 8):
    image = Image.new("L", (imgx, imgy))
    m = n % 2
    p = (n - m + 2.0) / 4.0
    q = p + 1.0
    a = 2.0 * math.pi / n
    b = a / 2.0 * (1.0 - m)
    x = 0.0
    y = 0.0

    for i in range(imgx * imgy):
        k = random.randint(0, n - 1)
        c = k * a + b
        x = (x + math.sin(c)) / q
        y = (y + math.cos(c)) / q
        kx = int((x * p + 1.0) / 2.0 * (imgx - 1))            
        ky = int((y * p + 1.0) / 2.0 * (imgy - 1))            
        image.putpixel((kx, ky), 255)

    image.save("rpIFSfr_" + str(n) + ".png", "PNG")
Tags: fractal, graphics, image, math

1 comment

FB36 (author) 14 years, 1 month ago  # | flag

Here is another type of the same fractals which I called Hexaflake-type:

# Regular Polygon IFS Fractals (Hexaflake-type)
# FB - 201003217
from PIL import Image
import math
import random

imgx = 512
imgy = 512

# coefficients of the t(n) (found using curve-fitting to experimentation data)
a0 =  1.1840972490170618e+01
b0 =  5.0562324258401986e-02
c0 = -1.3007278403313109e+01
d0 =  1.2962513369840259e-02
e0 =  4.6912973441805188e+06
f0 = -5.3565139656093468e+00

for n in range(3, 9): # triangle to octagon

    t = float(n) / ( a0 * math.exp(b0 * n) + c0 * math.exp(d0 * n) + e0 * math.exp(f0*n))

    image = Image.new("L", (imgx, imgy))
    m = n % 2
    p = (n - m + 2.0) / 4.0
    q = p + 1.0
    a = 2.0 * math.pi / n
    b = a / 2.0 * (1.0 - m)
    x = 0.0
    y = 0.0

    for i in range(imgx * imgy):
        k = random.randint(0, n)
        if k < n:
            c = k * a + b
            x = (x + math.sin(c)) / q
            y = (y + math.cos(c)) / q
        else:
            x = x / t
            y = y / t

        kx = int((x * p + 1.0) / 2.0 * (imgx - 1))            
        ky = int((y * p + 1.0) / 2.0 * (imgy - 1))            
        image.putpixel((kx, ky), 255)

    image.save("rpIFSfrHT_" + str(n) + ".png", "PNG")