Characterization of two-dimensional cellular automata over ternary fields


Siap I. , AKIN H., Sah F.

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, vol.348, no.7, pp.1258-1275, 2011 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 348 Issue: 7
  • Publication Date: 2011
  • Doi Number: 10.1016/j.jfranklin.2010.02.002
  • Title of Journal : JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
  • Page Numbers: pp.1258-1275

Abstract

The set of papers [3,4,6,7] (Chattopadhyay et al., 1999; Dihidar and Choudhury, 2004; Khan et al., 1997, 1999) deals with the behavior of the uniform two-dimensional cellular automata over binary fields (Z(2)). Some structural properties and precise mathematical models using matrix algebra over the field Z(2) are reported for characterizing the behavior of two-dimensional nearest neighborhood linear cellular automata with null and periodic boundary conditions [3,4,6,7] (Chattopadhyay et al., 1999; Dihidar and Choudhury, 2004; Khan et al., 1997, 1999). In this paper, we characterize two-dimensional linear cellular automata transformations by using matrix algebra built on Z(3). We analyze some results for two-dimensional CA with rule numbers 2460N and 2460P. Finally, we investigate the dimension of the kernel of two-dimensional cellular automata defined by the rule number 2460N. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.