Jean Pierre Boon
How fast does Langton's ant move?
(261K, tar.gz file)

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 ($c={\sqrt 2}/52$) follows exactly.