Squiral diffraction
Disordered Systems and Neural Networks
2019-10-03 v1 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.1211.5471,
title = {Squiral diffraction},
author = {Uwe Grimm and Michael Baake},
journal= {arXiv preprint arXiv:1211.5471},
year = {2019}
}
Comments
6 pages. 4 figures; talk presented at Aperiodic 2012 (Cairns). For a full mathematical treatment see arXiv:1205.1384