Generalized sub-shifts in elementary cellular automata: the “strange case” of chaotic rule 180
✍ Scribed by Gianpiero Cattaneo; Luciano Margara
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 924 KB
- Volume
- 201
- Category
- Article
- ISSN
- 0304-3975
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✦ Synopsis
We 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 OS 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).