Abstract

In this paper we show that a class of sets known as the Rauzy fractals, which are constructed via substitution dynamical systems, give rise to self-afine multi-tiles and self-afine tilings. This provides an eficient and unconventional way for constructing aperiodic self-afine tilings. Our result also leads to a proof that a Rauzy fractal R associated with a primitive and unimodular Pisot substitution has nonempty interior.

Authors