Substitutions, abstract number systems and the space filling property
Clemens Fuchs, Rob Tijdeman · Annales de l’institut Fourier · 2006
In this paper we study multi-dimensional words generated by fixed points of substitutions by projecting the integer points on the corresponding broken halfline. We show for a large class of substitutions that the resulting word is the restriction of a linear function modulo 1 and that it can be decided whether the resulting word is space filling or not. The proof uses lattices and the abstract number system associated with the substitution.