How fast does Langton's ant move?

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