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… (More)

Computing modular coincidences can show whether a given substitution system, which is supported on a point lattice in R, consists of model sets or not. We prove the computatibility of this problem… (More)

There are several notions of the ‘dual’ of a word/tile substitution. We show that the most common ones are equivalent for substitutions in dimension one, where we restrict ourselves to the case of… (More)

Two new series of substitution tilings are introduced in which the tiles appear in infinitely many orientations. It is shown that several properties of the well-known pinwheel tiling do also hold for… (More)

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 tilings of the Penrose… (More)

Two results about equidistribution of tile orientations in primitive substitution tilings are stated, one for finitely many, one for infinitely many orientations. Furthermore, consequences for the… (More)

This paper studies properties of tilings of the plane by parallelograms. In particular it is established that in parallelogram tilings using a finite number of shapes all tiles occur in only finitely… (More)

Pinwheel patterns and their higher dimensional generalisations display continuous circular or spherical symmetries in spite of being perfectly ordered. The same symmetries show up in the… (More)

Square triangle tilings are relevant models for quasicrystals. We introduce a new self-similar tile-substitution which yields the well-known nonperiodic square triangle tilings of Schlottmann. It is… (More)