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C*-algebras of tilings with infinite rotational symmetry

A tiling with infinite rotational symmetry, such as the Conway– 
Radin Pinwheel Tiling, gives rise to a topological dynamical system to which 
an etale equivalence relation is associated. A groupoid ´ C 
∗ 
-algebra for a tiling 
is produced and a separating dense set is exhibited in the C 
∗ 
-algebra which 
encodes the structure of the topological dynamical system. In the case of a 
substitution tiling, natural subsets of this separating dense set are used to de- 
fine an AT-subalgebra of the C 
∗ 
-algebra. Finally our results are applied to the 
Pinwheel Tiling.