Random noble means substitutions

TL;DR

This paper studies the properties of random noble mean substitutions, extending previous work on random Fibonacci sequences, and analyzes their dynamical systems, entropy, invariant measures, and diffraction spectra.

Contribution

It introduces a framework for analyzing random noble mean substitutions, extending the random Fibonacci model, and characterizes their dynamical and spectral properties.

Findings

Determined the entropy of the systems.

Identified ergodic invariant measures.

Analyzed the diffraction spectrum.

Abstract

The random local mixture of a family of primitive substitution rules with noble mean inflation multiplier is investigated. This extends the random Fibonacci example that was introduced by Godr\`{e}che and Luck in 1989. We discuss the structure of the corresponding dynamical systems, and determine their entropy, an ergodic invariant measure and diffraction spectrum.