Combinatorial and geometrical properties of a class of tilings - Messaoudi, A. (Belgian Mathematical Soc Triomphe, 2005)
In this paper, we consider a tiling generated by a Pisot unit number of degree d >= 3 which has a finite expansible property. We compute the states of a finite automaton which recognizes the boundary of the central tile. We also prove in the case d = 3 that the interior of each tile is simply connected.
Keywords: tiling; automata; Pisot number