36327
2012
2012
eng
83
113
31
2
7
article
Old City Publishing Science
Philadelphia
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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.
Journal of cellular automata
1557-5969 (print)
wos:2011-2013
WOS:000302978700002
Gutschow, J (reprint author), Leibniz Univ Hannover, Inst Theoret Phys, D-30167 Hannover, Germany., nesme@qipc.org
Deutsche Forschungsgemeinschaft [Forschergruppe 635]; EU; Erwin
Schrodinger Institute; Rosa Luxemburg Foundation
Johannes Guetschow
Vincent Nesme
Reinhard F. Werner
eng
uncontrolled
fractal
eng
uncontrolled
abelian group
eng
uncontrolled
linear cellular automaton
eng
uncontrolled
substitution system
eng
uncontrolled
self-similarity
Institut für Physik und Astronomie
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