# Diffraction of a binary non-Pisot inflation tiling

## TL;DR

This paper investigates the diffraction properties of a family of one-dimensional binary inflation tilings, identifying conditions for pure point spectra and analyzing the nature of their diffraction spectra.

## Contribution

It characterizes all cases with pure point spectrum within the family and discusses the diffraction spectra of other members, highlighting the prevalence of singular continuous diffraction.

## Key findings

- Only the Fibonacci rule has pure point spectrum.
- Most other rules exhibit purely singular continuous diffraction.
- Bragg peaks are trivial except at the origin.

## Abstract

A one-parameter family of binary inflation rules in one dimension is considered. Apart from the first member, which is the well-known Fibonacci rule, no inflation factor is a unit. We identify all cases with pure point spectrum, and discuss the diffraction spectra of the other members of the family. Apart from the trivial Bragg peaks at the origin, they have purely singular continuous diffraction.