If you read books about Logo while you were a kid you remember all that fun with turtle graphics, using loops to draw circles and recursion to generate really complicated shapes.

As you can see on wikipedia drawing a Sierpinski carpet pixel by pixel is trivial when the squares are aligned to x & y axes. The general case is a bit harder. Here is how to do it with a turtle and a little bit of of recursion.

def carpet(r):
if r < 1:
return
penup()
forward(r / 2); left(90); forward(r / 2); right(90)
pendown();
for k in range(4):
right(90)
forward(r)
penup(); forward(r / 2); left(90); forward(r / 2); right(90)
for k in range(4):
carpet(r / 3)
right(90)
forward(r)
carpet(r / 3)
forward(r)
penup()
back(r)
right(90)
forward(r)
left(90)

Sierpinski carpet free rotation

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