On the Convergence of Elementary Cellular Automata under Sequential Update Modes
Discrete Mathematics
2026-02-25 v2
Abstract
In this paper, we perform a theoretical analysis of the sequential convergence of elementary cellular automata that have at least one fixed point. Our aim is to establish which elementary rules always reach fixed points under sequential update modes, regardless of the initial configuration. In this context, we classify these rules according to whether all initial configurations converge under all, some, one or none sequential update modes, depending on if they have fixed points under synchronous (or parallel) update modes.
Keywords
Cite
@article{arxiv.2509.07797,
title = {On the Convergence of Elementary Cellular Automata under Sequential Update Modes},
author = {Isabel Donoso-Leiva and Eric Goles and Martín Ríos-Wilson and Sylvain Sené},
journal= {arXiv preprint arXiv:2509.07797},
year = {2026}
}