2025/07/09 by Katariina Paturi, Paturi, Katariina
Biochemistry, Genetics and Molecular Biology · Computer Science · #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Formal Methods in Verification #Gene Regulatory Network Analysis
paper · pdf · doi:10.48550/arxiv.2507.06896
openalex publication_date 2025/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Non-uniform cellular automata (NUCA) are an extension of cellular automata (CA), which transform cells according to multiple different local rules. A NUCA is defined by a configuration of local rules called a local rule distribution. We examine what properties of uniform CA can be recovered by restricting the rule distribution to be (uniformly) recurrent, focusing on only 1D NUCA. We show that a bijective NUCA with a uniformly recurrent rule distribution is reversible. We also show that if a NUCA is surjective and has a recurrent rule distribution, or if it is bijective, then it is balanced. We present an example of a NUCA which has a non-empty and non-residual set of equicontinuity points, and one which is not sensitive but has no equicontinuity points. Finally, we show that (positively) expansive NUCA are sensitive.