Three variations on a theme by Fibonacci

Baake, Michael; Frank, Natalie Priebe and Grimm, Uwe (2021). Three variations on a theme by Fibonacci. Stochastics and Dynamics, 21(3), article no. 2140001.

DOI: https://doi.org/10.1142/S0219493721400013

Abstract

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 renormalisation structure. It allows explicit calculations, particularly in cases where one meets regular model sets with Rauzy fractals as windows.

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About

• Item ORO ID
• 69853
• Item Type
• Journal Item
• ISSN
• 0219-4937
• Project Funding Details

• Funded Project Name	Project ID	Funding Body
  Lyapunov Exponents and Spectral Properties of Aperiodic Structures	EP/S010335/1	EPSRC (Engineering and Physical Sciences Research Council)

• Keywords
• inflation tilings; dynamical spectrum; diffraction; cocycle; Rauzy fractals
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM)
  Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
• Copyright Holders
• © 2021 Michael Baake, © 2021 Natalie Priebe Frank, © 2021 Uwe Grimm
• Depositing User
• Uwe Grimm