2012/03/18 by Vladimir Garcı́a-Morales, Garcia-Morales, Vladimir
Computer Science · Mathematics · #Cellular Automata and Applications #Cellular Automata and Lattice Gases (nlin.CG) #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.1203.3939
openalex publication_date 2012/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A universal map is derived for all deterministic 1D cellular automata (CA) containing no freely adjustable parameters. The map can be extended to an arbitrary number of dimensions and topologies and its invariances allow to classify all CA rules into equivalence classes. Complexity in 1D systems is then shown to emerge from the weak symmetry breaking of the addition modulo an integer number p. The latter symmetry is possessed by certain rules that produce Pascal simplices in their time evolution. These results elucidate Wolfram's classification of CA dynamics.