SCD Patterns Have Singular Diffraction
arXiv:math-ph/0411052 · doi:10.1063/1.1842355
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.
11 pages, 2 figures; Accepted for Journal of Mathematical Physics