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arXiv · 0808.1732

Pattern formation in growing sandpiles

Deepak Dhar·Tridib Sadhu·Samarth Chandra
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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.

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Deepak Dhar, Tridib Sadhu, Samarth Chandra. 2008-08-12. Pattern formation in growing sandpiles. https://doi.org/10.1209/0295-5075%2F85%2F48002

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