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arXiv · 2605.22762

Minimality, transitivity and sensitivity of non-uniform cellular automata

Supreeti Kamilya·Jarkko Kari·Katariina Paturi
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Abstract

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.

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Supreeti Kamilya, Jarkko Kari, Katariina Paturi. 2026-05-21. Minimality, transitivity and sensitivity of non-uniform cellular automata. https://arxiv.org/abs/2605.22762

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