1993/11/01 by K Eloranta, Kari Eloranta · 4 citations
Computer Science · Materials Science · Mathematics · #Cellular Automata and Applications #Mathematical Dynamics and Fractals #Quasicrystal Structures and Properties
paper · doi:10.1088/0951-7715/6/6/010
openalex publication_date 1993/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
One-dimensional cellular automata are analysed via their generalized permutivity. Invariant subalphabets provide a systematic way of identifying periodic and aperiodic tilings as well as stationary distributions invariant under the cellular automaton iteration. In the case of several invariant subalphabets a hierarchy of interaction phenomena arise. In particular the interaction of subalphabets can generate random walks as well as their degenerate forms. A comprehensive scheme emerges that unifies the analysis of topological defects in cellular automata. The probabilistic details of the random walks involved are treated in the companion paper in this issue.