Limiting behaviour of linear cellular automata
type: Item
instance of: scholarly article
title: Limiting behaviour of linear cellular automata
zbMATH Open document ID: 0632.68052
author: Satoshi Takahashi
published in: Proceedings of the Japan Academy. Series A
publication date: 1987-01-01T00:00:00Z
review text: In the present paper the limiting behaviour of d-dimensional linear M- state cellular automata (d-LCA) is investigated. d-LCA are defined by local transition functions F of the type \[ F(x_ 1,x_ 2,...,x_ n)=\sum^{n}_{i=1}a_ ix_ i\quad (mod M)\quad, \] where \(a_ i,x_ i\in \{0,1,...,M-1\}\) and \(x_ i\) \((i=1,...,n)\) are the states of all neighbours of an arbitrary machine in the cellular structure. For the class of these automata the author shows that every d-LCA has a limit set of finite configurations. A detailed investigation of d-LCA can be found in the book [Parallel processing systems (V. Alad'ev (ed.)), Valgus Press. Tallinn (1983)].
Mathematics Subject Classification ID: 68Q80
zbMATH DE Number: 4028908
zbMATH Keywords: limiting behaviour
zbMATH Keywords: cellular automata
MaRDI profile type: Publication
full work available at URL: pjaa.63.182
OpenAlex ID: W2055150808
cites work: Cellular automata can generate fractals
cites work: Congruence properties of ordinary and q-binomial coefficients
cites work: Geometry of Binomial Coefficients
cites work: Statistical mechanics of cellular automata
DOI: 10.3792/PJAA.63.182
description: scientific article; zbMATH DE number 4028908