English

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 NN as N\sqrt{N}. We give exact characterization of the asymptotic pattern, in terms of the position and shape of different features of the pattern.

Keywords

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

R2 v1 2026-06-21T11:09:48.716Z