On sand automata

Abstract

In this paper we introduce sand automata in order to give a common and useful framework for the study of most of the models of sandpiles. Moreover we give the possibility to have sources and sinks of "sand grains". We prove a result which shows that the class of sand automata is rich enough to simulate any reasonable model of sandpiles based on local interaction rules. We also give an algorithm to find the fixed points of the evolutions of the sandpiles. Finally we prove that reversibility is equivalent to bijectivity. © Springer-Verlag Berlin Heidelberg 2003.