Abstract

We perform intensive simulations of the model known as Generalised Langton’s Ants, discovering rules with a large number of highways. We depict the structure of some of them, formally proving that there is no universal bound on the number of highways which are possible for a given ant rule, and even that some ant rules have infinitely many highways. In particular we disprove the belief that the propagation speed of a given ant’s highways is uniquely determined. Our simulations show that, for some rules, different highways appear with very unequal frequencies, in some cases only a few times in a billion runs. This suggests that those highways that appear as the only possible asymptotic behaviour of some rules, might be accompanied by several very infrequent highways which are very hard to find. © The Author(s), under exclusive licence to Springer Nature B.V. 2025.