Ants on the highway
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866918207314460672 |
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| author | Gajardo, Anahí Lutfalla, Victor Rao, Michaël |
| author_facet | Gajardo, Anahí Lutfalla, Victor Rao, Michaël |
| contents | We perform intensive computations of Generalised Langton's Ants, discovering rules with a big number of highways. We depict the structure of some of them, formally proving that the number of highways which are possible for a given rule does not need to be bounded, moreover it can be infinite. The frequency of appearing of these highways is very unequal within a given generalised ant rule, in some cases these frequencies where found in a ratio of $1/10^7$ in simulations, suggesting that those highways that appears as the only possible asymptotic behaviour of some rules, might be accompanied by a big family of very infrequent ones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_10124 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ants on the highway Gajardo, Anahí Lutfalla, Victor Rao, Michaël Discrete Mathematics We perform intensive computations of Generalised Langton's Ants, discovering rules with a big number of highways. We depict the structure of some of them, formally proving that the number of highways which are possible for a given rule does not need to be bounded, moreover it can be infinite. The frequency of appearing of these highways is very unequal within a given generalised ant rule, in some cases these frequencies where found in a ratio of $1/10^7$ in simulations, suggesting that those highways that appears as the only possible asymptotic behaviour of some rules, might be accompanied by a big family of very infrequent ones. |
| title | Ants on the highway |
| topic | Discrete Mathematics |
| url | https://arxiv.org/abs/2409.10124 |