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arXiv · 1007.0707

Diffraction of limit periodic point sets

Michael Baake·Uwe Grimm
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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.

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Michael Baake, Uwe Grimm. 2010-07-05. Diffraction of limit periodic point sets. https://doi.org/10.1080/14786435.2010.508447

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