Anecdote: When I was in high school, I was <i>really</i> 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:<p><a href="http://joelgustafson.com/things/automata/?150" rel="nofollow">http://joelgustafson.com/things/automata/?150</a><p>If you are wondering, this is the trinomial triangle:<p><a href="https://en.wikipedia.org/wiki/Trinomial_triangle" rel="nofollow">https://en.wikipedia.org/wiki/Trinomial_triangle</a>