Self-similarity of cellular automata on abelian groups
- It is well known that the spacetime diagrams of some cellular automata have a self-similar fractal structure: for instance Wolfram's rule 90 generates a Sierpinski triangle. Explaining the self-similarity of the spacetime diagrams of cellular automata is a well-explored topic, but virtually all of the results revolve around a special class of automata, whose typical features include irreversibility, an alphabet with a ring structure, a global evolution that is a ring homomorphism, and a property known as (weakly) p-Fermat. The class of automata that we study in this article has none of these properties. Their cell structure is weaker, as it does not come with a multiplication, and they are far from being p-Fermat, even weakly. However, they do produce self-similar spacetime diagrams, and we explain why and how.
| Verfasserangaben: | Johannes Guetschow, Vincent Nesme, Reinhard F. Werner |
|---|---|
| ISSN: | 1557-5969 |
| Titel des übergeordneten Werks (Englisch): | Journal of cellular automata |
| Verlag: | Old City Publishing Science |
| Verlagsort: | Philadelphia |
| Publikationstyp: | Wissenschaftlicher Artikel |
| Sprache: | Englisch |
| Jahr der Erstveröffentlichung: | 2012 |
| Erscheinungsjahr: | 2012 |
| Datum der Freischaltung: | 26.03.2017 |
| Freies Schlagwort / Tag: | abelian group; fractal; linear cellular automaton; self-similarity; substitution system |
| Band: | 7 |
| Ausgabe: | 2 |
| Seitenanzahl: | 31 |
| Erste Seite: | 83 |
| Letzte Seite: | 113 |
| Fördernde Institution: | Deutsche Forschungsgemeinschaft [Forschergruppe 635]; EU; Erwin Schrodinger Institute; Rosa Luxemburg Foundation |
| Organisationseinheiten: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
| Peer Review: | Referiert |
