Ants on the highway
Discrete Mathematics
2025-11-19 v1
Abstract
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 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.
Cite
@article{arxiv.2409.10124,
title = {Ants on the highway},
author = {Anahí Gajardo and Victor Lutfalla and Michaël Rao},
journal= {arXiv preprint arXiv:2409.10124},
year = {2025}
}