Pattern formation in growing sandpiles

Abstract

Adding grains at a single site on a flat substrate in the Abelian sandpile models produce beautiful complex patterns. We study in detail the pattern produced by adding grains on a two-dimensional square lattice with directed edges (each site has two arrows directed inward and two outward), starting with a periodic background with half the sites occupied. The size of the pattern formed scales with the number of grains added $N$ as $\sqrt{N}$. We give exact characterization of the asymptotic pattern, in terms of the position and shape of different features of the pattern.

5 pages, 4 figures, submitted to Phys. Rev. Lett

References in corpus (2)

• Limiting shapes for deterministic centrally seeded growth models
• Explicit characterization of the identity configuration in an Abelian Sandpile Model

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