Advances in Symmetric Sandpiles

Article type: Research Article

Authors: Formenti, Enrico | Masson, Benoît | Pisokas, Theophilos

Affiliations: Laboratoire I3S, Université de Nice-Sophia Antipolis, Bât. ESSI, 930 route des Colles, 06903 Sophia Antipolis Cedex, France. E-mail: {enrico.formenti,benoit.masson}@unice.fr,[email protected]

Abstract: A symmetric version of the well-known SPM model for sandpiles is introduced. We prove that the new model has fixed-point dynamics. Although there might be several fixed points, a precise description of the fixed points is given. Moreover, we provide a simple closed formula for counting the number of fixed points originated by initial conditions made of a single column of grains. Bounds for the transient length are also given.

Keywords: discrete dynamical systems, SOC systems, sandpiles, fixed point dynamics, transient length

Journal: Fundamenta Informaticae, vol. 76, no. 1-2, pp. 91-112, 2007