2024/08/13 by Naoto Shiraishi, Shiraishi, Naoto, Shinji Takesue +1
Computer Science · #Cellular Automata and Applications #Cellular Automata and Lattice Gases (nlin.CG) #Computability, Logic, AI Algorithms #FOS: Physical sciences #Quantum-Dot Cellular Automata #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2408.06691
openalex publication_date 2024/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.