# Sierpinski Square combination fractal using recursion.
# (Combination of Sierpinski Square and 2 other square fractals!)
# FB - 201008102
from PIL import Image, ImageDraw
imgx = 2187
imgy = 2187
image = Image.new("L", (imgx, imgy))
draw = ImageDraw.Draw(image)
def ssf (x, y, a): # Sierpinski square fractal
global draw
# draw rectangle
draw.line ([(int(x), int(y)),(int(x + a), int(y))], 255)
draw.line ([(int(x), int(y)),(int(x), int(y + a))], 255)
draw.line ([(int(x), int(y + a)),(int(x + a), int(y + a))], 255)
draw.line ([(int(x + a), int(y)),(int(x + a), int(y + a))], 255)
a = float(a) / 3
if a < 1: return
for j in range(3):
for k in range(3):
if not( k == 1 and j == 1):
ssf(x + a * k, y + a * j, a)
def s0 (x, y, a): # top-left
ssf(x, y, a)
b = float(a) / 3
if b < 1: return
s0(x - b, y - b, b) # top-left
s1(x - b, y + a, b) # bottom-left
s2(x + a, y - b, b) # top-right
def s1 (x, y, a): # bottom-left
ssf(x, y, a)
b = float(a) / 3
if b < 1: return
s0(x - b, y - b, b) # top-left
s1(x - b, y + a, b) # bottom-left
s3(x + a, y + a, b) # bottom-right
def s2 (x, y, a): # top-right
ssf(x, y, a)
b = float(a) / 3
if b < 1: return
s0(x - b, y - b, b) # top-left
s2(x + a, y - b, b) # top-right
s3(x + a, y + a, b) # bottom-right
def s3 (x, y, a): # bottom-right
ssf(x, y, a)
b = float(a) / 3
if b < 1: return
s1(x - b, y + a, b) # bottom-left
s2(x + a, y - b, b) # top-right
s3(x + a, y + a, b) # bottom-right
def t0 (x, y, a): # top
ssf(x, y, a)
b = float(a) / 3
if b < 1: return
t0(x + b, y - b, b) # top
t2(x - b, y + b, b) # left
t3(x + a, y + b, b) # right
def t1 (x, y, a): # bottom
ssf(x, y, a)
b = float(a) / 3
if b < 1: return
t1(x + b, y + a, b) # bottom
t2(x - b, y + b, b) # left
t3(x + a, y + b, b) # right
def t2 (x, y, a): # left
ssf(x, y, a)
b = float(a) / 3
if b < 1: return
t0(x + b, y - b, b) # top
t1(x + b, y + a, b) # bottom
t2(x - b, y + b, b) # left
def t3 (x, y, a): # right
ssf(x, y, a)
b = float(a) / 3
if b < 1: return
t0(x + b, y - b, b) # top
t1(x + b, y + a, b) # bottom
t3(x + a, y + b, b) # right
# MAIN
mx2 = imgx / 2
my2 = imgy / 2
my4 = my2 / 2
# center Sierpinski square
ssf(mx2 - my4, my2 - my4, my2)
# 4 corners
s0(mx2 - my4 - my2 / 3, my2 - my4 - my2 / 3, my2 / 3) # top-left
s1(mx2 - my4 - my2 / 3, my2 - my4 + my2 , my2 / 3) # bottom-left
s2(mx2 - my4 + my2 , my2 - my4 - my2 / 3, my2 / 3) # top-right
s3(mx2 - my4 + my2 , my2 - my4 + my2 , my2 / 3) # bottom-right
# 4 sides
t0(mx2 - my4 + my2 / 3, my2 - my4 - my2 / 3, my2 / 3) # top
t1(mx2 - my4 + my2 / 3, my2 - my4 + my2 , my2 / 3) # bottom
t2(mx2 - my4 - my2 / 3, my2 - my4 + my2 / 3, my2 / 3) # left
t3(mx2 - my4 + my2 , my2 - my4 + my2 / 3, my2 / 3) # right
image.save("SqPlusSq3.png", "PNG")
