88 citations · 95 across the 5 of their papers we have counts for
5 papers
Root lattices and quasicrystals
M. Baake, D. Joseph, P. Kramer +1
It is shown how root lattices and their reciprocals might serve as the right pool for the construction of quasicrystalline structure models. All non-periodic symmetries observed so…
Averaged shelling for quasicrystals
Michael Baake, Uwe Grimm, Dieter Joseph +1
The shelling of crystals is concerned with counting the number of atoms on spherical shells of a given radius and a fixed centre. Its straight-forward generalization to quasicrysta…
Trace maps, invariants, and some of their applications
Michael Baake, Uwe Grimm, Dieter Joseph
Trace maps of two-letter substitution rules are investigated with special emphasis on the underlying algebraic structure and on the existence of invariants. We illustrate the resul…
Modelling Quasicrystal Growth
Uwe Grimm, Dieter Joseph
Understanding the growth of quasicrystals poses a challenging problem, not the least because the quasiperiodic order present in idealized mathematical models of quasicrystals prohi…
Coordination Sequences and Critical Points
Michael Baake, Uwe Grimm, Przemyslaw Repetowicz +1
Coordination sequences of periodic and quasiperiodic graphs are analysed. These count the number of points that can be reached from a given point of the graph by a number of steps…