Anahí GajardoUdeC, Victor LutfallaI2M, Michaël RaoLIP
{"title":"公路上的蚂蚁","authors":"Anahí GajardoUdeC, Victor LutfallaI2M, Michaël RaoLIP","doi":"arxiv-2409.10124","DOIUrl":null,"url":null,"abstract":"We perform intensive computations of Generalised Langton's Ants, discovering\nrules with a big number of highways. We depict the structure of some of them,\nformally proving that the number of highways which are possible for a given\nrule does not need to be bounded, moreover it can be infinite. The frequency of\nappearing of these highways is very unequal within a given generalised ant\nrule, in some cases these frequencies where found in a ratio of $1/10^7$ in\nsimulations, suggesting that those highways that appears as the only possible\nasymptotic behaviour of some rules, might be accompanied by a big family of\nvery infrequent ones.","PeriodicalId":501216,"journal":{"name":"arXiv - CS - Discrete Mathematics","volume":"11 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Ants on the highway\",\"authors\":\"Anahí GajardoUdeC, Victor LutfallaI2M, Michaël RaoLIP\",\"doi\":\"arxiv-2409.10124\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We perform intensive computations of Generalised Langton's Ants, discovering\\nrules with a big number of highways. We depict the structure of some of them,\\nformally proving that the number of highways which are possible for a given\\nrule does not need to be bounded, moreover it can be infinite. The frequency of\\nappearing of these highways is very unequal within a given generalised ant\\nrule, in some cases these frequencies where found in a ratio of $1/10^7$ in\\nsimulations, suggesting that those highways that appears as the only possible\\nasymptotic behaviour of some rules, might be accompanied by a big family of\\nvery infrequent ones.\",\"PeriodicalId\":501216,\"journal\":{\"name\":\"arXiv - CS - Discrete Mathematics\",\"volume\":\"11 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - CS - Discrete Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.10124\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - CS - Discrete Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10124","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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.
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