I explored fractals based on an n-by-n pattern like this one:
To make the fractal, I replaced each black square with the entire pattern, and then repeated this process multiple times. The L-shaped pattern above results in this Sierpinski fractal:
That turns out to be the only interesting fractal based on a 2-by-2 pattern. Things got more interesting when I moved onto 3-by-3 patterns like this one, in which only the middle square is empty:
That pattern resulted in this carpet fractal:
I had seen that fractal before, but I found there were many other interesting fractals based on 3-by-3 patterns. Here are a few of my favorites:
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