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arXiv · 2408.06691

Complete ergodicity in one-dimensional reversible cellular automata

Naoto Shiraishi·Shinji Takesue
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Abstract

Exactly ergodicity in boundary-driven semi-infinite cellular automata (CA) are investigated. We establish all the ergodic rules in CA with 3, 4, and 5 states. We analytically prove the ergodicity for 12 rules in 3-state CA and 118320 rules in 5-state CA with any ergodic and periodic boundary condition, and numerically confirm all the other rules non-ergodic with some boundary condition. We classify ergodic rules into several patterns, which exhibit a variety of ergodic structure.

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Naoto Shiraishi, Shinji Takesue. 2024-08-13. Complete ergodicity in one-dimensional reversible cellular automata. https://doi.org/10.1007/s10955-025-03529-3

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