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It generates a fractal from any given IFS definition (Fractint style).

Python, 78 lines
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# IFS fractals
# FB - 201003221
from PIL import Image
import random

### 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]]

### Fractint IFS definition of Dragon
##mat = [[0.824074, 0.281482, -0.212346,  0.864198, -1.882290, -0.110607, 0.787473],
##       [0.088272, 0.520988, -0.463889, -0.377778,  0.785360,  8.095795, 0.212527]]

### Levy C curve
##mat = [[0.5, -0.5, 0.5, 0.5, 0.0, 0.0, 0.5],
##       [0.5, 0.5, -0.5, 0.5, 0.5, 0.5, 0.5]]

# Levy Dragon
mat = [[0.5, -0.5, 0.5, 0.5, 0.0, 0.0, 0.5],
       [-0.5, -0.5, 0.5, -0.5, 1.0, 0.0, 0.5]]

# image size
imgx = 512
imgy = 512 # will be auto-re-adjusted

m = len(mat)
# find the xmin, xmax, ymin, ymax
x = mat[0][4]
y = mat[0][5] 
#
xa = x
xb = x
ya = y
yb = y
# 
for k in range(imgx * imgy):
    p=random.random()
    psum = 0.0
    for i in range(m):
        psum += mat[i][6]
        if p <= psum:
            break
    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 
    #
    if x < xa:
        xa = x
    if x > xb:
        xb = x
    if y < ya:
        ya = y
    if y > yb:
        yb = y

# drawing
imgy = round(imgy * (yb - ya) / (xb - xa)) # auto-re-adjust the aspect ratio 
image = Image.new("L", (imgx, imgy))

x=0.0
y=0.0 
for k in range(imgx * imgy):
    p=random.random()
    psum = 0.0
    for i in range(m):
        psum += mat[i][6]
        if p <= psum:
            break
    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("IFS_.png", "PNG")

2 comments

Michael Fogleman 11 years, 8 months ago  # | flag

I tested it out with the Fern and the Dragon. Looks nice!

FB36 (author) 11 years, 8 months ago  # | flag

If anyone interested, download an old (DOS/Win) version of Fractint zip file from http://spanky.triumf.ca/www/fractint/getting.html, extract the fractint.ifs file from it to get many more IFS fractal definitions (which easily can be converted to draw w/ this code).

Created by FB36 on Sun, 21 Mar 2010 (MIT)
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