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Talk Abstract
Langton's Ant: a Toy Model for Low Dimensional Reactive Processes

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)
    http://www.ma.utexas.edu/cgi-bin/mp\_arc/ 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))
    http://rene.ma.utexas.edu/mp\_arc/ Paper 99-171

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