Transient and cyclic behavior of cellular automata with null boundary conditions

Document Type

Article

Publication Date

10-1-1993

Abstract

One-dimensional cellular automata (CA) over finite fields are studied in which each interior cell is updated to contain the sum of the previous values of its two nearest neighbors. Boundary cells are updated according to null boundary conditions. For a given initial configuration, the CA evolves through transient configurations to an attracting cycle. The dependence of the maximal transient length and maximal cycle length on the number of cells is investigated. Both can be determined from the minimal polynomial of the update matrix, which in this case satisfies a useful recurrence relation. With cell values from a field of characteristic two, the explicit dependence of the maximal transient length on the number of cells is determined. Extensions and directions for future work are presented. © 1993 Plenum Publishing Corporation.

Identifier

21844440360 (Scopus)

Publication Title

Journal of Statistical Physics

External Full Text Location

https://doi.org/10.1007/BF01052755

e-ISSN

15729613

ISSN

00224715

First Page

159

Last Page

174

Issue

1-2

Volume

73

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