How fast does Langton's ant move?
arXiv:cond-mat/0004331
Abstract
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 () follows exactly.
8 pages incl. 1 figure; submitted to J.Stat.Phys