Diffraction of a model set with complex windows

Baake, Michael and Grimm, Uwe (2020). Diffraction of a model set with complex windows. Journal of Physics: Conference Series, 1458 pp. 1–6.

DOI: https://doi.org/10.1088/1742-6596/1458/1/012006


The well-known plastic number substitution gives rise to a ternary inflation tiling of the real line whose inflation factor is the smallest Pisot-Vijayaraghavan number. The corresponding dynamical system has pure point spectrum, and the associated control point sets can be described as regular model sets whose windows in two-dimensional internal space are Rauzy fractals with a complicated structure. Here, we calculate the resulting pure point diffraction measure via a Fourier matrix cocycle, which admits a closed formula for the Fourier transform of the Rauzy fractals, via a rapidly converging infinite product.

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