On the Addition of Recurrent Configurations of the Sandpile-Model

Authors:
Matthias Schulz
Affiliations:
Department for Computer Sciences, University of Karlsruhe, Karlsruhe, Germany 76128
Venue:
ACRI '08 Proceedings of the 8th international conference on Cellular Automata for Reseach and Industry
Year:
2008

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Abstract

The sandpile model, introduced by Bak, Tang and Wiesenfeld in 1987, is the standard example for a dynamic model showing Self-Organized Criticality (SOC). Also, it has many nice algebraic properties; for example, there is a set of configurations which is a group with a certain naturally defined addition.We look at elements c, dof this group and try to find out how long it takes to naively compute the sum c茂戮驴 d. While we can easily give an upper bound, it is harder to find a lower bound. We prove some facts about the number of topplings (elementary operations) that have to be performed during the addition of two elements of the group and give a heuristic for quickly finding local minima.