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Diffraction of limit periodic point sets
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 MagazineVolume
91Issue
19-21Pagination
2661-2670ISSN
1478-6435Department/School
School of Natural SciencesPublisher
Taylor & FrancisPlace of publication
Mortimer House, 37-41 Mortimer Street, London W1TRights statement
Copyright 2011 Taylor & FrancisRepository Status
- Restricted