Langton's Ant: a Toy Model for Low Dimensional Reactive Rrocesses

Thursday, June 8, 2000 - 3:30pm - 4:30pm
Keller 3-180
Jean-Pierre Boon (Université Libre de Bruxelles)
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. Despite the simplicity of its basic algorithm, Langton's ant has remained a puzzle in terms of analytical description. Insight can be gained from the one-dimensional and the triangular two-dimensional versions of this automaton for which analytical calculations can be performed, and interesting properties can be proved. We suggest that this class of simple automata may provide a prototype model for low-dimensional reactive processes.

Related papers :

Jean Pierre Boon: How fast does Langton's ant move?
(submitted to the Journal of Statistical Physics) Paper 00-189

Patrick Grosfils, Jean Pierre Boon, E.G.D. Cohen, L.A. Bunimovich:
Propagation and organization in lattice random media
(J. Stat. Phys. {bf 97}, 575 (1999)) Paper 99-171