Eur. Phys. J. B 16, 501-505 (2000)
https://doi.org/10.1007/s100510070209

Growth exponent in the Domany-Kinzel cellular automaton

Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, CP 702, 30123-970, Belo Horizonte, MG - Brazil

Corresponding authors: ^a atman@fisica.ufmg.br - ^b jmoreira@ipe.fisica.ufmg.br

Received: 15 March 2000
Published online: 15 August 2000

Abstract

In a roughening process, the growth exponent β describes how the roughness w grows with the time t: w∼t^β. We determine the exponent β of a growth process generated by the spatiotemporal patterns of the one-dimensional Domany-Kinzel cellular automaton. The values obtained for β show a cusp at the frozen/active transition which permits determination of the transition line. The β value at the transition depends on the scheme used: symmetric (β≈0.83) or non-symmetric (β≈0.61). Using damage spreading ideas, we also determine the active/chaotic transition line; this line depends on how the replicas are updated.