A tiling has statistical circular symmetry, if the orientation of the tiles of each kind are equidistributed on the unit sphere. It is shown in [Fre08] that all primitive substitution tilings with tiles in infinitely many orientations are of statistical circular symmetry. For a precise definition of statistical circular symmetry, see [Fre08] .
[fre08]
Frettlöh, D.
Substitution tilings with statistical circular symmetry
European Journal of Combinatorics
2008,
29,
pp. 1881-1893,
arxiv 0704.2521