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Mathematical aspects of quasicrystals

About substitution tilings with statistical circular symmetry

Pages 2033-2039 | Received 28 Sep 2007, Accepted 21 Dec 2007, Published online: 11 Oct 2010
 

Abstract

Two results about equidistribution of tile orientations in primitive substitution tilings are stated, one for finitely many, and one for infinitely many orientations. Furthermore, consequences for the associated diffraction spectra and the dynamical systems are discussed.

Acknowledgements

It is a pleasure to thank Christoph Richard for many helpful comments. This work was supported by the German Research Council (DFG), within the CRC 701.

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