Limiting behaviour of linear cellular automata (Q1095664)

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)].