Anecdote: When I was in high school, I was really bored in class on day, and I started writing out the trinomial triangle modulo 2; I was curious as to whether or not it followed a similar pattern to Pascal's triangle modulo 2. Lo and behold, what emerged was Rule 150:
There are several variations on Sierpinski's triangle; rule 60 or rule 210 are others. Rule 150 is different. It is also a fractal but with a very different pattern.
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If you are wondering, this is the trinomial triangle:
https://en.wikipedia.org/wiki/Trinomial_triangle