Details
| Original language | Undefined/Unknown |
|---|---|
| Title of host publication | Proceedings of Automata 2010 |
| Editors | Nazim Fatès, Jarkko Kari, Thomas Worsch |
| Pages | 51-70 |
| Number of pages | 20 |
| Publication status | Published - 2010 |
Abstract
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Proceedings of Automata 2010. ed. / Nazim Fatès; Jarkko Kari; Thomas Worsch. 2010. p. 51-70.
Research output: Chapter in book/report/conference proceeding › Contribution to book/anthology › Research › peer review
}
TY - CHAP
T1 - The fractal structure of cellular automata on Abelian groups
AU - Gütschow, Johannes
AU - Nesme, Vincent
AU - Werner, Reinhard F.
PY - 2010
Y1 - 2010
N2 - It is well-known that the spacetime diagrams of some cellular automata have a fractal structure: for instance Pascal's triangle modulo 2 generates a Sierpinski triangle. Explaining the fractal structure of the spacetime diagrams of cellular automata is a much 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 fractal spacetime diagrams, and we explain why and how.
AB - It is well-known that the spacetime diagrams of some cellular automata have a fractal structure: for instance Pascal's triangle modulo 2 generates a Sierpinski triangle. Explaining the fractal structure of the spacetime diagrams of cellular automata is a much 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 fractal spacetime diagrams, and we explain why and how.
M3 - Beitrag in Buch/Sammelwerk
SP - 51
EP - 70
BT - Proceedings of Automata 2010
A2 - Fatès, Nazim
A2 - Kari, Jarkko
A2 - Worsch, Thomas
ER -