On the Fibonacci Tiling and its Modern Ramifications

In the last 30 years, the mathematical theory of aperiodic order has developed enormously. Many new tilings and properties have been discovered, few of which are covered or anticipated by the early papers and books. Here, we start from the well‐known Fibonacci chain to explain some of them, with poi...

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Bibliographic Details
Published inIsrael journal of chemistry Vol. 64; no. 10-11
Main Authors Baake, Michael, Gähler, Franz, Mazáč, Jan
Format Journal Article
LanguageEnglish
Published 01.11.2024
Subjects
diffraction
dynamical systems
embedding method
Mathematical quasicrystals
model sets
Rauzy fractals
spectral theory
substitution and inflation
topological aspects
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Summary:In the last 30 years, the mathematical theory of aperiodic order has developed enormously. Many new tilings and properties have been discovered, few of which are covered or anticipated by the early papers and books. Here, we start from the well‐known Fibonacci chain to explain some of them, with pointers to various generalisations as well as to higher‐dimensional phenomena and results. This should give some entry points to the modern literature on the subject.
ISSN:0021-2148
1869-5868
DOI:10.1002/ijch.202300155