my main webpage is http://mathcenter.spb.ru/nikaan/
you can check how tropical curves (and hypersurfaces, in general) emerge from abelian sandpile models: Tropical curves and sandpiles
popular article about sandpiles in Spanish http://universo.math.org.mx/2015-3/Pilas/arena.html
arXiv web page http://arxiv.org/find/all/1/all:+AND+Nikita+Kalinin/0/1/0/all/0/1