Pattern formation in growing sandpiles
Statistical Mechanics
2010-10-01 v1
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 as . We give exact characterization of the asymptotic pattern, in terms of the position and shape of different features of the pattern.
Cite
@article{arxiv.0808.1732,
title = {Pattern formation in growing sandpiles},
author = {Deepak Dhar and Tridib Sadhu and Samarth Chandra},
journal= {arXiv preprint arXiv:0808.1732},
year = {2010}
}
Comments
5 pages, 4 figures, submitted to Phys. Rev. Lett