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Three variations on a theme by Fibonacci

Research paper by Michael Baake, Natalie Priebe Frank, Uwe Grimm

Indexed on: 01 Nov '20Published on: 14 Apr '20Published in: Stochastics and Dynamics



Abstract

Stochastics and Dynamics, Ahead of Print. Several variants of the classic Fibonacci inflation tiling are considered in an illustrative fashion, in one and in two dimensions, with an eye on changes or robustness of diffraction and dynamical spectra. In one dimension, we consider extension mechanisms of deterministic and of stochastic nature, while we look at direct product variations in a planar extension. For the pure point part, we systematically employ a cocycle approach that is based on the underlying renormalization structure. It allows explicit calculations, particularly in cases where one meets regular model sets with Rauzy fractals as windows.