Interactive Torus Parametrization of the One-Dimensional Fibonacci Quasicrystal

Mykhailo Koreshkov; Maryna Nesterenko

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arXiv · 2609.33863

Interactive Torus Parametrization of the One-Dimensional Fibonacci Quasicrystal

Mykhailo Koreshkov·Maryna Nesterenko

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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.

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Mykhailo Koreshkov, Maryna Nesterenko. 2026-09-27. Interactive Torus Parametrization of the One-Dimensional Fibonacci Quasicrystal. https://arxiv.org/abs/2609.33863

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