On the Fibonacci tiling and its modern ramifications
Metric Geometry
2025-01-29 v2 Mathematical Physics
math.MP
Abstract
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.
Cite
@article{arxiv.2311.05387,
title = {On the Fibonacci tiling and its modern ramifications},
author = {Michael Baake and Franz Gähler and Jan Mazáč},
journal= {arXiv preprint arXiv:2311.05387},
year = {2025}
}
Comments
13 pages, 10 figures; introductory overview, written for the proceedings of ICQ 15; revised and slightly extended version