A1 Refereed original research article in a scientific journal
On the surjunctivity and the Garden of Eden theorem for non-uniform cellular automata
Authors: Paturi, Katariina; Kari, Jarkko
Publisher: Springer Science and Business Media LLC
Publication year: 2026
Journal: Natural Computing
Article number: 9
Volume: 25
Issue: 1
ISSN: 1567-7818
eISSN: 1572-9796
DOI: https://doi.org/10.1007/s11047-026-10067-8
Publication's open availability at the time of reporting: Open Access
Publication channel's open availability : Partially Open Access publication channel
Web address : https://doi.org/10.1007/s11047-026-10067-8
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/515869756
Self-archived copy's licence: CC BY
Self-archived copy's version: Publisher`s PDF
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.
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Funding information in the publication:
Open Access funding provided by University of Turku (including Turku University Central Hospital
