Some comments on pinwheel tilings and their diffraction

Details Some comments on pinwheel tilings and their diffraction Some comments on pinwheel tilings and their diffraction

2011-02-08

arxiv.org/abs/1102.1750v1

Journal of Physics: Conference Series 284 (2011) 012032

Physics

Mathematical Physics

9 pages, 9 figures

Scientific paper

10.1088/1742-6596/284/1/012032

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.

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