There there "elementary" resources on [Penrose Tilings][1] in relation to [noncommutative geometry][2]?  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][3]


  [1]: http://en.wikipedia.org/wiki/Penrose_tiling
  [2]: http://www.alainconnes.org/docs/book94bigpdf.pdf
  [3]: http://www.jdawiseman.com/papers/trivia/penrose_tiling.png