Interactive Torus Parametrization of the One-Dimensional Fibonacci Quasicrystal
Abstract
We present an interactive computational framework for exploring the torus parametrization of the one-dimensional Fibonacci quasicrystal and its local hull. While cut-and-project schemes and Fourier analysis of local functions have been actively explored, a purely algebraic treatment still requires deeper geometric intuition regarding the underlying dynamical systems to advance these methods further. We develop an open-source interactive Python/Jupyter tool that links coordinates in the fundamental domain of the embedding lattice directly to the physical tiling and word generation, offering a transparent visual analysis of translation orbits and singular boundary cases. The tool is the basis for our further computational work, and it can also be used in teaching and to illustrate the geometry of the local hull.
Related
- High-dimensional extreme eigenvalue problems: low-rank tensor parametrization and optimization
- Random self-similar series on the two-dimensional torus
- Sharp Strichartz estimates on the one-dimensional torus
- Limit law for Brownian cover time of the two dimensional torus
- Exotic operators on the Hardy spaces of the infinite-dimensional torus
BibTeX
@misc{koreshkov2026interactive,
title = {{Interactive Torus Parametrization of the One-Dimensional Fibonacci Quasicrystal}},
author = {Mykhailo Koreshkov and Maryna Nesterenko},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33863},
eprint = {2609.33863},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33863},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Interactive Torus Parametrization of the One-Dimensional Fibonacci Quasicrystal
AU - Mykhailo Koreshkov
AU - Maryna Nesterenko
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33863
UR - https://arxiv.org/abs/2609.33863
AB - We present an interactive computational framework for exploring the torus parametrization of the one-dimensional Fibonacci quasicrystal and its local hull. While cut-and-project schemes and Fourier analysis of local functions have been actively explored, a purely algebraic treatment still requires deeper geometric intuition regarding the underlying dynamical systems to advance these methods further. We develop an open-source interactive Python/Jupyter tool that links coordinates in the fundamental domain of the embedding lattice directly to the physical tiling and word generation, offering a transparent visual analysis of translation orbits and singular boundary cases. The tool is the basis for our further computational work, and it can also be used in teaching and to illustrate the geometry of the local hull.
ER -