# Diffraction of a model set with complex windows

Research paper by Michael Baake, Uwe Grimm

Indexed on: 13 Feb '20Published on: 10 Feb '20Published in: Journal of physics. Conference series

#### Abstract

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.