How fast does Langton's ant move?

Details How fast does Langton's ant move? How fast does Langton's ant move?

2000-04-19

arxiv.org/abs/cond-mat/0004331v1

Physics

Condensed Matter

Statistical Mechanics

8 pages incl. 1 figure; submitted to J.Stat.Phys

Scientific paper

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.

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