New C*-algebras from substitution tilings

Given a tiling with finite local complexity and a finite number of patterns up to translation, we associate a C*-algebra to it. We show that this C* -algebra is a recursive subhomogeneous algebra and characterize its ideals. In the case of a substitution tiling, that also has primitivity and recognizability, we use the construction mentioned above, on each of the inflated tilings, to obtain a inductive limit C*-algebra that encodes the dynamics of the inflation map. We show that this C* -algebra is simple.