Volume 85, Number 4, February 2009
Article Number 48002
Number of page(s) 6
Section Interdisciplinary Physics and Related Areas of Science and Technology
Published online 05 March 2009
EPL, 85 (2009) 48002
DOI: 10.1209/0295-5075/85/48002

Pattern formation in growing sandpiles

Deepak Dhar, Tridib Sadhu and Samarth Chandra

Department of Theoretical Physics, Tata Institute of Fundamental Research 1 Homi Bhaba Road, Mumbai 400005 India

received 1 January 2009; accepted in final form 3 February 2009; published February 2009
published online 5 March 2009

Adding grains at a single site on a flat substrate in the Abelian sandpile models produces 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 model shows proportionate growth and the size of the pattern formed by adding N grains scales as $\sqrt{N} $. We give exact characterization of the asymptotic pattern, in terms of the position and shape of different features of the pattern.

89.75.Kd - Complex systems: Patterns.
45.70.Cc - Static sandpiles; granular compaction.

© EPLA 2009