Abstract
Conway and Radin's ``quaquaversal'' tiling of R 3 is known to exhibit statistical rotational symmetry in the infinite volume limit. A finite patch, however, cannot be perfectly isotropic, and we compute the rates at which the anisotropy scales with size. In a sample of volume N , tiles appear in O(N 1/6 ) distinct orientations. However, the orientations are not uniformly populated. A small (O(N 1/84 ) ) set of these orientations account for the majority of the tiles. Furthermore, these orientations are not uniformly distributed on SO(3) . Sample averages of functions on SO(3) seem to approach their ergodic limits as N -1/336 . Since even macroscopic patches of a quaquaversal tiling maintain noticeable anisotropy, a hypothetical physical quasicrystal whose structure was similar to the quaquaversal tiling could be identified by anisotropic features of its electron diffraction pattern.
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