TY  - JOUR
A1  - Guetschow, Johannes
A1  - Nesme, Vincent
A1  - Werner, Reinhard F.
T1  - Self-similarity of cellular automata on abelian groups
JF  - Journal of cellular automata
N2  - 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.
KW  - fractal
KW  - abelian group
KW  - linear cellular automaton
KW  - substitution system
KW  - self-similarity
Y1  - 2012
SN  - 1557-5969
VL  - 7
IS  - 2
SP  - 83
EP  - 113
PB  - Old City Publishing Science
CY  - Philadelphia
ER  -