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Coalescing Cellular Automata: Synchronization by Common Random Source for Asynchronous Updating
Jean-Baptiste Rouquier and Michel Morvan

We say that a Cellular Automaton (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, non coalescence for two other, and show that there exist 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.

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