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Article

Pattern formation and tropical geometry

Sandpile model exhibits fascinating pattern structures: patches, characterized by quadratic functions, and line-shaped patterns (also called solitons, webs, or linear defects). It was predicted by Dhar and Sadhu that sandpile patterns with line-like features may be described in terms of tropical geometry. We explain the main ideas and technical tools -- tropical geometry and discrete superharmonic functions -- used to rigorously establish certain properties of these patterns. It seems that the aforementioned tools have great potential for generalizing and applying in a variety of situations.