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arXiv · 2507.06896

Reversibility, balance and expansivity of non-uniform cellular automata

Katariina Paturi
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Abstract

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.

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Katariina Paturi. 2025-07-09. Reversibility, balance and expansivity of non-uniform cellular automata. https://arxiv.org/abs/2507.06896

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