2025/07/09 by Katariina Paturi, Paturi, Katariina, Jarkko Kari +1
Computer Science · Mathematics · #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Formal Methods in Verification #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2507.06987
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 with multiple local rules in different cells. We show that if the distribution of local rules is uniformly recurrent, or recurrent in the one-dimensional case, the Garden of Eden theorem holds. We also show that for any non-recurrent distribution, there is a substitution of local rules that defines a NUCA which does not satisfy the Garden of Eden theorem. Finally, we show that a rule distribution asymptotic to recurrent distribution defines a surjunctive NUCA.