Reversibility, balance and expansivity of non-uniform cellular automata
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908442262765568 |
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| author | Paturi, Katariina |
| author_facet | Paturi, Katariina |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06896 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reversibility, balance and expansivity of non-uniform cellular automata Paturi, Katariina Dynamical Systems 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. |
| title | Reversibility, balance and expansivity of non-uniform cellular automata |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2507.06896 |