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Fern IFS Fractal (Python recipe) by FB36
ActiveState Code (http://code.activestate.com/recipes/577134/)

Fern Fractal drawn using its Fractint IFS definition.

Python, 42 lines
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# Fern IFS fractal
# FB - 201003217
from PIL import Image
import random

imgx = 512
imgy = 512
image = Image.new("L", (imgx, imgy))

# Fractint IFS definition of Fern
mat=[[0.0,0.0,0.0,0.16,0.0,0.0,0.01],
    [0.85,0.04,-0.04,0.85,0.0,1.6,0.85],
    [0.2,-0.26,0.23,0.22,0.0,1.6,0.07],
    [-0.15,0.28,0.26,0.24,0.0,0.44,0.07]]

xa = -5.5
xb = 6.5
ya = -0.5
yb = 10.5

x=0.0
y=0.0 
for k in range(imgx * imgy):

    p=random.random() 
    if p <= mat[0][6]:
        i=0 
    elif p <= mat[0][6] + mat[1][6]:
        i=1 
    elif p <= mat[0][6] + mat[1][6] + mat[2][6]:
        i=2 
    else:
        i=3 

    x0 = x * mat[i][0] + y * mat[i][1] + mat[i][4] 
    y  = x * mat[i][2] + y * mat[i][3] + mat[i][5] 
    x = x0 
    jx = int((x - xa) / (xb - xa) * (imgx - 1)) 
    jy = (imgy - 1) - int((y - ya) / (yb - ya) * (imgy - 1))
    image.putpixel((jx, jy), 255) 

image.save("fern.png", "PNG")
Tags: fractal, graphics, image, math