Squiral diffraction

Abstract

The Thue-Morse system is a paradigm of singular continuous diffraction in one dimension. Here, we consider a planar system, constructed by a bijective block substitution rule, which is locally equivalent to the squiral inflation rule. For balanced weights, its diffraction is purely singular continuous. The diffraction measure is a two-dimensional Riesz product that can be calculated explicitly.

6 pages. 4 figures; talk presented at Aperiodic 2012 (Cairns). For a full mathematical treatment see arXiv:1205.1384

References in corpus (3)

• Mathematical diffraction of aperiodic structures
• Squirals and beyond: Substitution tilings with singular continuous spectrum
• The singular continuous diffraction measure of the Thue-Morse chain

Cited by in corpus (1)

• A note on measures vanishing at infinity