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://xxx.lanl.gov/abs/cond-mat/0004331
  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://xxx.lanl.gov/abs/cond-mat/9905168
  http://rene.ma.utexas.edu/mp\_arc/ Paper 99-171
  

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