A deterministic sandpile automaton revisited
Theoretische Physik, Gerhard-Mercator-Universität Duisburg, 47048 Duisburg,
2 Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903, USA
Published online: 15 February 2000
The Bak-Tang-Wiesenfeld (BTW) sandpile model is a cellular automaton which has been intensively studied during the last years as a paradigm for self-organized criticality. In this paper, we reconsider a deterministic version of the BTW model introduced by Wiesenfeld, Theiler and McNamara, where sand grains are added always to one fixed site on the square lattice. Using the Abelian sandpile formalism we discuss the static properties of the system. We present numerical evidence that the deterministic model is only in the BTW universality class if the initial conditions and the geometric form of the boundaries do not respect the full symmetry of the square lattice.
PACS: 64.60.Ht – Dynamic critical phenomena / 05.65.+b – Self-organized systems / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000