Diffraction of limit periodic point sets

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.

10 pages, 2 figures; paper presented at ICQ11 (Sapporo)

References in corpus (3)

• An aperiodic hexagonal tile
• Can Kinematic Diffraction Distinguish Order from Disorder?
• The singular continuous diffraction measure of the Thue-Morse chain

Cited by in corpus (15)

• Hyperuniform States of Matter
• Mathematical diffraction of aperiodic structures
• Hidden Multiscale Order in the Primes
• Kinematic Diffraction from a Mathematical Viewpoint
• Spectral and topological properties of a family of generalised Thue-Morse sequences
• Aperiodic crystals and beyond
• Uncovering Multiscale Order in the Prime Numbers via Scattering
• The structure factor of primes
• Hyperuniformity Classes of Quasiperiodic Tilings via Diffusion Spreadability
• Close-packed dimers on the line: diffraction versus dynamical spectrum
• Emergence of limit-periodic order in tiling models
• On arithmetic progressions in non-periodic self-affine tilings
• Hierarchical freezing in a lattice model
• Homometry in the light of coherent beams
• Hyperuniformity and anti-hyperuniformity in one-dimensional substitution tilings