Complete ergodicity in one-dimensional reversible cellular automata

Autor:	Shiraishi, Naoto, Takesue, Shinji
Rok vydání:	2024
Předmět:	Nonlinear Sciences - Cellular Automata and Lattice Gases Condensed Matter - Statistical Mechanics
Druh dokumentu:	Working Paper
Popis:	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. Comment: 63 pages, 47 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2408.06691 Zobrazit plný text záznamu View this record from Arxiv