Cellular automaton model of self-healing
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913551397945344 |
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| author | Fukś, Henryk Soto, José Manuel Gómez |
| author_facet | Fukś, Henryk Soto, José Manuel Gómez |
| contents | We propose a simple cellular automaton model of a self-healing system and investigate its properties. In the model, the substrate is a two-dimensional checkerboard configuration which can be damaged by changing values of a finite number of sites. The cellular automaton we consider is a checkerboard voting rule, a binary rule with Moore neighbourhood which is topologically conjugate to majority voting rule. For a single color damage (when only cells in the same state are modified), the rule always fixes the damage. For a general damage, when it is localized inside a $3 \times 3$ square, the rule also fixes it always. When the damage is inside of a larger $n \times n$ square, the efficiency of the rule in fixing the damage becomes smaller than $100\%$, but it remains better than $98\%$ for $n \leq 5$ and better than $75 \%$ for $n\leq 7$. We show that in the limit of infinite $n$ the efficiency tends to zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_13689 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cellular automaton model of self-healing Fukś, Henryk Soto, José Manuel Gómez Cellular Automata and Lattice Gases 68Q80 We propose a simple cellular automaton model of a self-healing system and investigate its properties. In the model, the substrate is a two-dimensional checkerboard configuration which can be damaged by changing values of a finite number of sites. The cellular automaton we consider is a checkerboard voting rule, a binary rule with Moore neighbourhood which is topologically conjugate to majority voting rule. For a single color damage (when only cells in the same state are modified), the rule always fixes the damage. For a general damage, when it is localized inside a $3 \times 3$ square, the rule also fixes it always. When the damage is inside of a larger $n \times n$ square, the efficiency of the rule in fixing the damage becomes smaller than $100\%$, but it remains better than $98\%$ for $n \leq 5$ and better than $75 \%$ for $n\leq 7$. We show that in the limit of infinite $n$ the efficiency tends to zero. |
| title | Cellular automaton model of self-healing |
| topic | Cellular Automata and Lattice Gases 68Q80 |
| url | https://arxiv.org/abs/2410.13689 |