Minimality, transitivity and sensitivity of non-uniform cellular automata
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866918516759724032 |
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| author | Kamilya, Supreeti Kari, Jarkko Paturi, Katariina |
| author_facet | Kamilya, Supreeti Kari, Jarkko Paturi, Katariina |
| contents | Every transitive cellular automaton (CA) is sensitive to initial conditions. We study this implication in the more general context of non-uniform cellular automata (NUCA) with finitely many different local update rules assigned to cells. We construct a two-dimensional NUCA that is minimal -- and hence transitive -- but that is not sensitive to initial conditions. The construction is based on an odometer NUCA on $\{0,1,2\}^\mathbb{N}$ which is nearly uniform in the sense that only the first cell uses a different local rule. Then we show that if the assignment of local rules in the cells is recurrent then transitivity implies sensitivity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_22762 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Minimality, transitivity and sensitivity of non-uniform cellular automata Kamilya, Supreeti Kari, Jarkko Paturi, Katariina Dynamical Systems Every transitive cellular automaton (CA) is sensitive to initial conditions. We study this implication in the more general context of non-uniform cellular automata (NUCA) with finitely many different local update rules assigned to cells. We construct a two-dimensional NUCA that is minimal -- and hence transitive -- but that is not sensitive to initial conditions. The construction is based on an odometer NUCA on $\{0,1,2\}^\mathbb{N}$ which is nearly uniform in the sense that only the first cell uses a different local rule. Then we show that if the assignment of local rules in the cells is recurrent then transitivity implies sensitivity. |
| title | Minimality, transitivity and sensitivity of non-uniform cellular automata |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2605.22762 |