Coalescing Cellular Automata

  • Jean-Baptiste Rouquier
  • Michel Morvan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3993)


We say that a Cellular Automata (CA) is coalescing when its execution on two distinct (random) initial configurations in the same asynchronous mode (the same cells are updated in each configuration at each time step) makes both configurations become identical after a reasonable time. We prove coalescence for two elementary rules and show that there exists infinitely many coalescing CA. We then conduct an experimental study on all elementary CA and show that some rules exhibit a phase transition, which belongs to the universality class of directed percolation.


Random Walk Cellular Automaton Cellular Automaton Universality Class Full Disagreement 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jean-Baptiste Rouquier
    • 1
  • Michel Morvan
    • 1
    • 2
  1. 1.ENS Lyon, LIPLyonFrance
  2. 2.EHESS and Santa Fe Institute 

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