Are there "elementary" resources on Penrose Tilings in relation to noncommutative geometry? It's all a big blur to me. There are two transformations S and T that can grow the tilings and every tiling corresponds to a sequence of S's and T's. Somehow, there is a C* algebra related to this.

Can the elements of this algebra be interpreted as observables in a quantum mechanical system? What is the "geometry" of this noncommutative space?

Penrose Tiling http://www.jdawiseman.com/papers/trivia/penrose_tiling.png