Preprint 2024-22
Anahi Gajardo, Victor H. Lutfalla, Michaël Rao:
Ants on the highway
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. Our simulations show that for some rules different highways appear with very unequal frecuencies, in some cases in a ratio of 2/1 000 000 000, suggesting that those highways that appear as the only possible asymptotic behaviours of some rules, might be accompanied by several very infrequent highways which are very hard to find.
