Sandpile Burning Bijection & Spanning Trees

The abelian sandpile group on a grid has a beautiful bijection with spanning trees via the "burning algorithm." A stable sandpile configuration is recurrent iff it passes the burning test — and recurrent configs biject with spanning trees of the graph.

Sandpile (grains per cell)

Spanning Tree (burning order)

Click "Add Sand" to add grains, then topple to stable, then run the burning test.