Combinatorial and geometrical properties of a class of tilings
Ali Messaoudi · Bulletin of the Belgian Mathematical Society - Simon Stevin · 2005
In this paper, we consider a tiling generated by a Pisot unit number of degree $d \geq 3$ 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.