Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 83-113 |
| Seitenumfang | 31 |
| Fachzeitschrift | Journal of cellular automata |
| Jahrgang | 7 |
| Ausgabenummer | 2 |
| Publikationsstatus | Veröffentlicht - 2012 |
Abstract
It is well known that the spacetime diagrams of some cellular automata have a self-similar fractal structure: for instanceWolfram'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.
ASJC Scopus Sachgebiete
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- Steuerungs- und Systemtechnik
- Informatik (insg.)
- Allgemeine Computerwissenschaft
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in: Journal of cellular automata, Jahrgang 7, Nr. 2, 2012, S. 83-113.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Self-similarity of cellular automata on abelian groups
AU - Gütschow, Johannes
AU - Nesme, Vincent
AU - Werner, Reinhard F.
PY - 2012
Y1 - 2012
N2 - It is well known that the spacetime diagrams of some cellular automata have a self-similar fractal structure: for instanceWolfram'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.
AB - It is well known that the spacetime diagrams of some cellular automata have a self-similar fractal structure: for instanceWolfram'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.
KW - Abelian group
KW - Fractal
KW - Linear cellular automaton
KW - Self-similarity
KW - Substitution system
UR - http://www.scopus.com/inward/record.url?scp=84859474798&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:84859474798
VL - 7
SP - 83
EP - 113
JO - Journal of cellular automata
JF - Journal of cellular automata
SN - 1557-5969
IS - 2
ER -