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:
http://joelgustafson.com/things/automata/?150
If you are wondering, this is the trinomial triangle:
https://en.wikipedia.org/wiki/Trinomial_triangle