Some rigorous results for the Greenberg-Hastings Model


Journal Article

In this paper, we obtain some rigorous results for a cellular automaton known as the Greenberg-Hastings Model. The state space is {0, 1, 2}Zd. The dynamics are deterministic and discrete time. A site which is 1 changes to 2, a site which is 2 changes to 0, and a site which is 0 changes to a 1 if one of its 2 d neighbors is a 1. In one dimension, we compute the exact asymptotic rate at which the system dies out when started at random and compute the topological entropy. In two or more dimensions we show that starting from a nontrivial product measure, the limit exists as 3 m→∞ and is Bernoulli shift. Finally, we investigate the behavior of the system on a large finite box. © 1991 Plenum Publishing Corporation.

Full Text

Duke Authors

Cited Authors

  • Durrett, R; Steif, JE

Published Date

  • October 1, 1991

Published In

Volume / Issue

  • 4 / 4

Start / End Page

  • 669 - 690

Electronic International Standard Serial Number (EISSN)

  • 1572-9230

International Standard Serial Number (ISSN)

  • 0894-9840

Digital Object Identifier (DOI)

  • 10.1007/BF01259549

Citation Source

  • Scopus