The Biggest Identity Sandpiles and How to Compute Them
eavan.blogWhen 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.
The precursor to this blog entry, was discussed here: https://news.ycombinator.com/item?id=46210044 Shamefully, I somehow missed out on the discussion and can longer reply.
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.
A few of your links point to the previous Abelian sandpile blog post, but use the `.md` extension instead of `.html`.
Good catch, I've just fixed it now. Thanks
Cool. I didn't know the term before. It's basically like Conway's game of life with a different update rule.
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.
Cool stuff, thanks
I'm getting a PR_CONNECT_RESET_ERROR for this site - anybody else or is that just me?
Let me take a quick look. There is definitely other 2XX traffic, but I'll double check I haven't messed up any configs on the cdn.
This is so cool.
Reminds of the 2-player game named "Chain Reaction".
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.
The idea of [Abelian Sandpiles] seems very intriguing. Can you recommend some sources to read more about its theory?