You may have seen pictures of 1-dim cellular automata and some look semi-chaotic, but I was surprised that quite a few interesting, precise facts can be said about CA like **Rule 30**: https://www.youtube.com/watch?v=HcGjCcLEgN4 while other basic questions have not been answered. Another slightly related fun fact is that the **Collatz sequence** is also a rather simple local cellular automaton which displays similar patterns (see image). And the question whether it has a non-trivial cycle boils down to whether you can fabricate an infinite empty triangle.