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
define an AT-subalgebra of the C*-algebra. Finally our results are applied to
the Pinwheel Tiling
