Super cool stuff. I guess time to convergence is also fixed, since the distribution's second moments increase consistently.
It's an unrealistic model of diffusion; 4 grains of sand in a vertical stack do not spread out leaving 0 at the node where the stack used to be.
Nor even spread to a neighbor of the same height, but that’s ok, is just an idea.
The article acknowledges this
< ...real piles of sand don’t generate this kind of spontaneous structure. The abelian sandpile model doesn’t even try to capture the behavior of actual physical materials
it's extremely fast, and result is quite good too.
It was used quite heavily in the upcoming dune for ex