The automaton known as `Langton's ant' exhibits a dynamical transition from a disordered phase to an ordered phase where the particle dynamics (the ant) produces a regular periodic pattern (called `highway'). Despite the simplicity of its basic algorithm, Langton's ant has remained a puzzle in terms of analytical description. Here I show that the highway dynamics obeys a discrete equation where from the speed of the ant (c=2/52) follows exactly.
Cite
@article{arxiv.cond-mat/0004331,
title = {How fast does Langton's ant move?},
author = {Jean Pierre Boon},
journal= {arXiv preprint arXiv:cond-mat/0004331},
year = {2007}
}