On the Convergence of Elementary Cellular Automata under Sequential Update Modes
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866911463603437568 |
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| author | Donoso-Leiva, Isabel Goles, Eric Ríos-Wilson, Martín Sené, Sylvain |
| author_facet | Donoso-Leiva, Isabel Goles, Eric Ríos-Wilson, Martín Sené, Sylvain |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07797 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Convergence of Elementary Cellular Automata under Sequential Update Modes Donoso-Leiva, Isabel Goles, Eric Ríos-Wilson, Martín Sené, Sylvain Discrete Mathematics 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. |
| title | On the Convergence of Elementary Cellular Automata under Sequential Update Modes |
| topic | Discrete Mathematics |
| url | https://arxiv.org/abs/2509.07797 |