4 papers · 1 filter
Model sets: a survey
Robert V. Moody
This article surveys the mathematics of the cut and project method as applied to point sets, called here {\em model sets}. It covers the geometric, arithmetic, and analytical sides…
Lattice Substitution Systems and Model Sets
Jeong-Yup Lee, Robert V. Moody
The paper studies ways in which the sets of a partition of a lattice in $\RR^n$ become regular model sets. The main theorem gives equivalent conditions which assure that a matrix s…
Diffraction from visible lattice points and k-th power free integers
Michael Baake, Robert V. Moody, Peter A. B. Pleasants
We prove that the set of visible points of any lattice of dimension at least 2 has pure point diffraction spectrum, and we determine the diffraction spectrum explicitly. This settl…
Similarity submodules and root systems in four dimensions
Michael Baake, Robert V. Moody
Lattices and Z-modules in Euclidean space possess an infinitude of subsets that are images of the original set under similarity transformation. We classify such self-similar images…