一维可逆窖藏自动机的完全遍历性

arXiv - PHYS - Cellular Automata and Lattice Gases Pub Date : 2024-08-13 DOI:arxiv-2408.06691

Naoto Shiraishi, Shinji Takesue

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引用次数: 0

摘要

我们研究了边界驱动半无限蜂窝自动机（CA）中的精确遍历性。我们建立了 3、4 和 5 态 CA 中的所有遍历规则。我们分析证明了 3 态 CA 中的 12 条规则和 5 态 CA 中的 118320 条规则在任意遍历和周期边界条件下的遍历性，并用数值证实了所有其他规则在某些边界条件下的非遍历性。我们将遍历规则分为几种模式，它们表现出多种多样的遍历结构。

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Complete ergodicity in one-dimensional reversible cellar automata

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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arXiv - PHYS - Cellular Automata and Lattice Gases

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