Topological chaos of universal elementary cellular automata rule

The dynamical behaviors of elementary cellular automata rule 110 are analyzed from the viewpoint of symbolic dynamics in the space of bi-infinite symbolic sequences. This paper conducts a rigorous analysis of the relationship between rules 110, 170 and 240 by applying blocking transformation and releasing transformation. Based on this result, the topological chaos of T110 induced by rule 110 is evaluated; that is, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$T_{110}^{9}$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$T_{110}^{16}$\end{document} are topologically mixing and possess the positive topological entropies on their respective subsystems. Therefore, it is natural to argue that the intrinsic complexity of rule 110 is high according to the usual measure of complexity organized around the symbolic dynamics of stationary symbol sequences. Finally, it is worth mentioning that the method presented in this paper is also applicable to other blocking transformation equivalences therein.