Details
| Original language | English |
|---|---|
| Pages (from-to) | 83-113 |
| Number of pages | 31 |
| Journal | Journal of cellular automata |
| Volume | 7 |
| Issue number | 2 |
| Publication status | Published - 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.
Keywords
- Abelian group, Fractal, Linear cellular automaton, Self-similarity, Substitution system
ASJC Scopus subject areas
- Engineering(all)
- Control and Systems Engineering
- Computer Science(all)
- General Computer Science
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In: Journal of cellular automata, Vol. 7, No. 2, 2012, p. 83-113.
Research output: Contribution to journal › Article › Research › 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 -