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SCD Patterns Have Singular Diffraction

Michael Baake·Dirk Frettlöh
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Abstract

Among the many families of nonperiodic tilings known so far, SCD tilings are still a bit mysterious. Here, we determine the diffraction spectra of point sets derived from SCD tilings and show that they have no absolutely continuous part, that they have a uniformly discrete pure point part on the z-axis, and that they are otherwise supported on a set of concentric cylinder surfaces around this axis. For SCD tilings with additional properties, more detailed results are given.

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Michael Baake, Dirk Frettlöh. 2004-11-15. SCD Patterns Have Singular Diffraction. https://doi.org/10.1063/1.1842355

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