Diffraction of Random Noble Means Words

TL;DR

This paper investigates the properties of random noble means substitutions, focusing on dynamical, ergodic, and spectral aspects, including diffraction, entropy, and subword frequencies.

Contribution

It introduces a cut and project framework for the associated point sets and analyzes their spectral diffraction properties, advancing understanding of random noble means words.

Findings

Determined subword frequencies and topological entropy.

Established ergodicity of the system.

Analyzed spectral diffraction measures.

Abstract

In this paper, several aspects of the random noble means substitution are studied. Beyond important dynamical facets as the frequency of subwords and the computation of the topological entropy, the important issue of ergodicity is addressed. From the geometrical point of view, we outline a suitable cut and project setting for associated point sets and present results for the spectral analysis of the diffraction measure.