Abelian Sandpile Identity Element & Tropical Geometry —
The abelian sandpile group on an n×n grid has a unique identity element: a configuration
that when added to any stable sandpile and relaxed returns that pile unchanged.
The identity exhibits striking fractal self-similarity and tropical (min-plus) algebraic structure.
Toppling rule: a cell with ≥4 chips fires one chip to each neighbor.
The identity element emerges from adding 6·(all-2s) and relaxing twice — revealing fractal boundaries
related to tropical curves. Colors: chip height 0–3 mapped to dark→bright spectrum.