The other day, my friend Dan Miller pointed me at a YouTube video of a cellular automaton playing Rock Paper Scissors. Nice, I thought, from a game-theory perspective, but not all that surprising. The fact that the game has three cyclical states makes it a classic example of an excitation wave, and CA models of excitation waves have been around for a while.

In an attempt at a witty reply, I suggested to him that the authors explore a little further, and try their code with Rock Paper Scissors Lizard Spock, the five-state equivalent game invented by Sam Kass and Karen Bryla, and then popularized by the sitcom, The Big Bang Theory.

Having sent the email, I then reflected on my words. Once I’d got over the fact that I’d turned myself into a kind of ironic meta-parody of an already ironic sitcom character, it occurred to me that it was an idea worth following up. First, I built a copy of the three state automaton as a test case. As you can see, below, it’s just not that jazzy, once you get over the spirals. The patterns are extremely stable.

After that, I tried out the five state game.

Far more exciting, IMO. Each stable three-cycle in the game can establish a patch of local dominance that the others can’t invade. However, if a five-cycle becomes established, it swarms across the board like a fungus, devouring everything in its wake. Awesome.

Of course, one can go further. Why stop at 5? After all, there’s no reason you can’t extend the pattern to a higher number of states. Does this mean that you can get excitation waves made out of sets of mutually dominating excitation waves? I leave that as a mystery for you to ponder.