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Zbl 0726.11020
Salon, Olivier
Quelles tuiles! (Pavages apériodiques du plan et automates bidimensionnels). (Aperiodic tilings of the plane and two-dimensional automata). (French)
[J] Sémin. Théor. Nombres Bordx., Sér. II 1, No.1, 1-26 (1989). ISSN 0989-5558

It is proved that the regular Robinson tiling of the plane [see {\it B. Gruenbaum} and {\it G. C. Shephard}, Tilings and patterns (New York 1987; Zbl 0601.05001)], restricted to a quadrant, can be viewed as a two- dimensional fixed point $(t(m,n))\sb{(m,n)\in {\bbfN}\sp 2}$ of a (2,2)- substitution. Actually, there are 48 subsequences of the form $(t(p\sp km+r,p\sp kn+s))\sb{m,n},k\in {\bbfN},\quad 0\le r,s<p\sp k$ with $p=2$ and the result follows from a theorem due to the author [Sémin. Théor. Nombres, Univ. Bordeaux I 1986/1987, Exp. No.4 (1987; Zbl 0653.10049)] which characterizes fixed points t of (p,p)-substitutions by the finiteness of the set of subsequences of the above type.
[P.Liardet (Marseille)]

MSC 2000:: *11B85 Automata sequences
05B45 Tessellation and tiling problems
68Q80 Cellular and array automata

Keywords: aperiodic tiling; 2-dimensional finite automata; regular Robinson tiling; fixed point; substitution

Citations: Zbl 0601.05001; Zbl 0653.10049

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