Tropical objects in sandpiles

A sandpile model on a graph $G$ is a simple cellular automata. A state of a sandpile model is a function from the vertices of $G$ to non-negative integer numbers, representing the number of grains at each vertex of $G$. Then a relaxation of a sandpile model is defined as a sequence of topplings: if a vertex of valency $k$ has at least $k$ grains, then it gives one grain to each of its neighbors, one repeats topplings while it is possible.
Surprisingly for a certain initial state (“a small perturbation of the maximal stable state”), the final picture represents tropical curves and tropical hypersurfaces. I will explain all the definitions, show pictures and if time permits, we can speak about ideas in the proofs.