Coarsening and Bifurcations in Wide-Range Two-Dimensional Totalistic Cellular Automata
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911585115570176 |
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| author | Bagnoli, Franco Mencarelli, Luca |
| author_facet | Bagnoli, Franco Mencarelli, Luca |
| contents | We investigate Boolean, totalistic cellular automata with a majority or frustrated majority vote rule, and an interaction range of variable span. These two models show a behavior which differs from the mean-field one. The majority vote model is characterized by the presence of absorbing states, and there is a related bifurcation according to the initial density, in agreement with the mean-field approximation. For initial density equal to $0.5$, however, the dynamics is dominated by a coarsening process, which stops when clusters with a definite curvature radius are established. For the frustrated majority vote model, the mean-field approximation gives chaotic oscillations or a limit cycle. Instead, we observe active patterns, with stable density. Above a certain critical value for the interacting radius there is a bifurcation of the asymptotic density as a function of the initial one. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_10082 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Coarsening and Bifurcations in Wide-Range Two-Dimensional Totalistic Cellular Automata Bagnoli, Franco Mencarelli, Luca Cellular Automata and Lattice Gases We investigate Boolean, totalistic cellular automata with a majority or frustrated majority vote rule, and an interaction range of variable span. These two models show a behavior which differs from the mean-field one. The majority vote model is characterized by the presence of absorbing states, and there is a related bifurcation according to the initial density, in agreement with the mean-field approximation. For initial density equal to $0.5$, however, the dynamics is dominated by a coarsening process, which stops when clusters with a definite curvature radius are established. For the frustrated majority vote model, the mean-field approximation gives chaotic oscillations or a limit cycle. Instead, we observe active patterns, with stable density. Above a certain critical value for the interacting radius there is a bifurcation of the asymptotic density as a function of the initial one. |
| title | Coarsening and Bifurcations in Wide-Range Two-Dimensional Totalistic Cellular Automata |
| topic | Cellular Automata and Lattice Gases |
| url | https://arxiv.org/abs/2604.10082 |