Generalized sub-shifts in elementary cellular automata: the “strange case” of chaotic rule 180

AbstractWe study the dynamical behavior of elementary cellular automaton 180. This rule gives rise to a global dynamics on the phase space of all one-dimensional bi-infinite configurations which is Devaney topologically chaotic. The dense sub-dynamical system of configurations in background of 0s is a generalized sub-shift, i.e., multiple sub-shift whose multiplicity constant depends on the initial configuration. This sub-dynamical system is deeply “stable” in the sense that the null configuration is a global attractor, but with some components of the chaotic behaviour (transitivity and unpredictability). The dense sub-dynamical system of configurations in background of 1s is a fractal-like system, with strongly chaotic components (expansivity)