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arXiv · 2509.07797

On the Convergence of Elementary Cellular Automata under Sequential Update Modes

Isabel Donoso-Leiva·Eric Goles·Martín Ríos-Wilson·Sylvain Sené
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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.

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Isabel Donoso-Leiva, Eric Goles, Martín Ríos-Wilson, Sylvain Sené. 2025-09-09. On the Convergence of Elementary Cellular Automata under Sequential Update Modes. https://arxiv.org/abs/2509.07797

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