Baake, Michael and Grimm, Uwe
(2011).
Diffraction of limit periodic point sets.
Philosophical Magazine, 91(19-21),
pp. 2661–2670.
(
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Abstract
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.
| Item Type: |
Journal Article
|
| Copyright Holders: |
2011 Taylor & Francis |
| ISSN: |
1478-6435 |
| Funders: |
Leverhulme Trust (Visiting Professorship Michael Baake) |
| Keywords: |
diffraction; autocorrelation; limit periodicity; substitution systems; integer inflation factors; pure point measures |
| Academic Unit/Department: |
Mathematics, Computing and Technology > Mathematics and Statistics |
| Item ID: |
28781 |
| Depositing User: |
Uwe Grimm
|
| Date Deposited: |
18 May 2011 12:41 |
| Last Modified: |
30 Nov 2012 16:52 |
| URI: |
http://oro.open.ac.uk/id/eprint/28781 |
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