6 papers
Counting perfect colourings of plane regular tilings
Dirk Frettlöh
A first step in investigating colour symmetries of periodic and nonperiodic patterns is determining the number of colours which allow perfect colourings of the pattern under consid…
About Substitution Tilings with Statistical Circular Symmetry
Dirk Frettlöh
Two results about equidistribution of tile orientations in primitive substitution tilings are stated, one for finitely many, one for infinitely many orientations. Furthermore, cons…
Self-dual tilings with respect to star-duality
Dirk Frettlöh
The concept of star-duality is described for self-similar cut-and-project tilings in arbitrary dimensions. This generalises Thurston's concept of a Galois-dual tiling. The dual til…
A radial analogue of Poisson's summation formula with applications to powder diffraction and pinwheel patterns
Michael Baake, Dirk Frettlöh, Uwe Grimm
Diffraction images with continuous rotation symmetry arise from amorphous systems, but also from regular crystals when investigated by powder diffraction. On the theoretical side,…
Pinwheel patterns and powder diffraction
Michael Baake, Dirk Frettlöh, Uwe Grimm
Pinwheel patterns and their higher dimensional generalisations display continuous circular or spherical symmetries in spite of being perfectly ordered. The same symmetries show up…
Duality of Model Sets Generated by Substitutions
D. Frettlöh
The nature of this paper is twofold: On one hand, we will give a short introduction and overview of the theory of model sets in connection with nonperiodic substitution tilings and…