Core Concepts
The dynamics of elementary cellular automaton 18 are characterized by persistent local patterns known as kinks. The authors determine the configurations of the generic limit set containing at most two kinks, showing that the three limit sets (limit set, generic limit set, and μ-limit set) of rule 18 are distinct.
Abstract
The paper studies the asymptotic dynamics of elementary cellular automaton 18 through its limit set, generic limit set, and μ-limit set.
Key highlights:
The dynamics of rule 18 are characterized by persistent local patterns called kinks. Kinks can only be destroyed in pairs and cannot be created.
The authors characterize the configurations of the generic limit set containing at most two kinks. They show that all words with no kinks, one kink, and certain words with two kinks occur in the generic limit set.
As a corollary, the authors prove that the three limit sets (limit set, generic limit set, and μ-limit set) of rule 18 are distinct.
The authors also discuss the conjecture of Grassberger and Lind regarding the density of particles in rule 18, and suggest that determining the generic limit set is a viable strategy toward partially resolving this conjecture.
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