一维斐波那契准晶的交互式环面参数化
Interactive Torus Parametrization of the One-Dimensional Fibonacci Quasicrystal
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中文总结 AI 辅助
本文提出一个交互式Python/Jupyter工具，用于可视化一维斐波那契准晶的环面参数化，连接嵌入格坐标与物理平铺，支持教学和后续计算研究。
中文摘要 AI 辅助
我们提出了一个交互式计算框架，用于探索一维斐波那契准晶及其局部壳的环面参数化。虽然切割投影方案和局部函数的傅里叶分析已被积极研究，但纯粹代数处理仍需要关于底层动力系统的更深入几何直觉，以进一步推进这些方法。我们开发了一个开源的交互式Python/Jupyter工具，将嵌入格基本域中的坐标直接与物理平铺和词生成联系起来，提供对平移轨道和奇异边界情况的透明可视化分析。该工具是我们进一步计算工作的基础，也可用于教学和说明局部壳的几何形状。
英文摘要
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.
发表机构
- Institute of Mathematics of NAS of Ukraine（乌克兰国家科学院数学研究所）
- University “Kyiv School of Economics”（基辅经济学院大学）
机构由 AI 辅助整理，请以论文原文为准。
