C*-algebras associated with Mauldin-Williams graphs

A Mauldin-Williams graph M is a generalization of an iterated function system by a directed graph. Its invariant set K plays the role of the self-similar set. We associate a C* -algebra O_M (K) with a Mauldin-Williams graph M and the invariant set K, laying emphasis on the singular points. We assume that the underlying graph G has no sinks and no sources. If M satisfies the open set condition in K, and G is irreducible and is not a cyclic permutation, then the associated C*-algebra O_M (K) is simple and purely infinite. We calculate the K-groups for some examples including the inflation rule of the Penrose tilings.