I didn't know about this game, looks fun.
I'm trying to think if knowledge of sandpile identities could help strategically in the game, somehow. But I can't see anything obvious.
Yes, the stabilisation process is like a cellular automaton.
However, in this case there are no infinite "games", all configurations eventually stabilise. But that doesn't make it less interesting. You can define similar setups on different grids, e.g. hexagonal, and get similar update rules and patterns.
When I wrote Beautiful Abelian Sandpiles (https://eavan.blog/posts/beautiful-sandpiles.html) I wanted to show off some nice images of large identity sandpiles. But the simple algorithm I used was horrendously slow. Showing a sandpile identity that was larger than 100 by 100 took multiple seconds! That's not good enough! I became obsessed with trying to find a faster way, all in an effort to compute bigger and bigger sandpile identities, bigger than anything anyone had seen before. In the end, I did exactly that.
LegionMammal978 wanted to see a proper description of the identity calculation methods. You can consider this sequel to the initial blog post as an answer.
I'm not excited that it's done in python. I've had experience with Aider struggling to display text as fast as the llm is spitting it out, though that was probably 6 months ago now.
