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Diffraction of limit periodic point sets

journal contribution
posted on 2023-05-17, 12:00 authored by Michael BaakeMichael Baake, Uwe Grimm
Limit periodic point sets are aperiodic structures with pure point diffraction supported on a countably, but not finitely generated Fourier module that is based on a lattice and certain integer multiples of it. Examples are cut and project sets with p-adic internal spaces. We illustrate this by explicit results for the diffraction measures of two examples with 2-adic internal spaces. The first and well-known example is the period doubling sequence in one dimension, which is based on the period doubling substitution rule. The second example is a weighted planar point set that is derived from the classic chair tiling in the plane. It can be described as a fixed point of a block substitution rule.

History

Publication title

Philosophical Magazine

Volume

91

Issue

19-21

Pagination

2661-2670

ISSN

1478-6435

Department/School

School of Natural Sciences

Publisher

Taylor & Francis

Place of publication

Mortimer House, 37-41 Mortimer Street, London W1T

Rights statement

Copyright 2011 Taylor & Francis

Repository Status

  • Restricted

Socio-economic Objectives

Expanding knowledge in the mathematical sciences

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