2023/08/24 by Hervé Sabrié, Sabrié, Hervé, Ilkka Törmä +1
Computer Science · Mathematics · #37B15 #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Formal Languages and Automata Theory (cs.FL) #Mathematical Dynamics and Fractals #Nonlinear Dynamics and Pattern Formation
paper · pdf · doi:10.48550/arxiv.2308.12744
openalex publication_date 2023/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the the asymptotic dynamics of elementary cellular automaton 18 through its limit set, generic limit set and μ-limit set. The dynamics of rule 18 are characterized by persistent local patterns known as kinks. We characterize the configurations of the generic limit set containing at most two kinks. As a corollary, we show that the three limit sets of rule 18 are distinct.