CATALAN NUMBERS, DYCK LANGUAGE AND TIME SERIES OF ELEMENTARY CELLULAR AUTOMATON OF RULE 56

摘要

A new approach to study the evolution complexity of cellular automata is proposed and explained thoroughly by an example of elementary cellular automaton of rule 56. Using the tools of distinct excluded blocks, computational search and symbolic dynamics, the mathematical structure underlying the time series generated from the elementary cellular automaton of rule 56 is analyzed and its complexity is determined, in which the Dyck language and Catalan numbers emerge naturally.