Pattern formation in growing sandpilesDeepak 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 . 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