Abstract
We rigorously prove a form of disorderresistance for a class of onedimensional cellular automaton rules, including some that arise as boundary dynamics of twodimensional solidification rules. Specifically, when started from a random initial seed on an interval of length L, with probability tending to one as L→∞, the evolution is a replicator. That is, a region of space–time of density one is filled with a spatially and temporally periodic pattern, punctuated by a finite set of other finite patterns repeated at a fractal set of locations. On the other hand, the same rules exhibit provably more complex evolution from some seeds, while from other seeds their behavior is apparently chaotic. A principal tool is a new variant of percolation theory, in the context of additive cellular automata from random initial states.
Original language  English 

Pages (fromto)  17311776 
Journal  Annals of Probability 
Volume  43 
Issue number  4 
DOIs  
Publication status  Published  3 Jun 2015 
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Profiles

Professor Alexander E Holroyd
Person: Academic