Jean Pierre Boon
How fast does Langton's ant move?
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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.