Another of my cellular automata. This one really surprised me with just how much self-organisation it manages. It keeps pulling itself into a sort of wavy squares pattern when you stir it up, and even after its tipping over into chaos. It also looks a lot like the Peirce Quincuncial at times ( math.ucr.edu/home/baez/week229.html )
This is still based purely on local rules (both in space and time). Each pixel has a value which changes based on the values of its 8 neighbours at the previous frame. It has no knowledge of what is further out in space or further back in time.