Several variants of the classic Fibonacci inflation tiling are considered in an illustrative fashion, in one and in two dimensions, with an eye on changes or robustness of diffraction and dynamical spectra. In one dimension, we consider extension mechanisms of deterministic and of stochastic nature, while we look at direct product variations in a planar extension. For the pure point part, we systematically employ a cocycle approach that is based on the underlying renormalization structure. It allows explicit calculations, particularly in cases where one meets regular model sets with Rauzy fractals as windows.

中文翻译：

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斐波那契主题的三个变体

经典斐波那契膨胀平铺的几种变体以说明性方式考虑，在一维和二维中，着眼于衍射和动态光谱的变化或鲁棒性。在一个维度中，我们考虑确定性和随机性质的扩展机制，同时我们研究平面扩展中的直接乘积变化。对于纯点部分，我们系统地采用了一种基于底层重整化结构的 cocycle 方法。它允许显式计算，特别是在遇到以 Rauzy 分形作为窗口的常规模型集的情况下。