Some comments on pinwheel tilings and their diffraction

Grimm, Uwe and Deng, Xinghua (2011). Some comments on pinwheel tilings and their diffraction. Journal of Physics: Conference Series, 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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