Work

On the surjunctivity and the Garden of Eden theorem for non-uniform cellular automata

Year: 2026

Type: article

Abstract: 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 one-dimensional 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 one-dimensional rule distribution asymptotic to recurrent distribution defines a surjunctive NUCA.

Source: Natural Computing

DOI: 10.1007/s11047-026-10067-8

Authors: Katariina Paturi, Jarkko Kari

Institution: University of Turku

Language: English

Topic: Cellular Automata and Applications

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: Turun Yliopisto