Some comments on pinwheel tilings and their diffraction

Abstract

The pinwheel tiling is the paradigm for a substitution tiling with circular symmetry, in the sense that the corresponding autocorrelation is circularly symmetric. As a consequence, its diffraction measure is also circularly symmetric, so the pinwheel diffraction consists of sharp rings and, possibly, a continuous component with circular symmetry. We consider some combinatorial properties of the tiles and their orientations, and a numerical approach to the diffraction of weighted pinwheel point sets.

9 pages, 9 figures

References in corpus (4)

• Can Kinematic Diffraction Distinguish Order from Disorder?
• A radial analogue of Poisson's summation formula with applications to powder diffraction and pinwheel patterns
• Aperiodic order and pure point diffraction
• Pinwheel patterns and powder diffraction