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Factorizable Language: From Dynamics to Biology

Using the tools of distinct excluded blocks, computational search and symbolic dynamics, the classification problem of all 256 elementary cellular automata is discussed from the point of view of time series generated by them, and examples in each class are provided to explain the methods used.

Complexity analysis of time series generated by elementary cellular automata

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.

QINDakang

Papers

Catalan numbers, dyck language and time series of elementary cellular automaton of rule 56