1 citations · 1 across the 5 of their papers we have counts for
5 papers
Self-similar Delone sets and Pisot numbers
Christoph Bandt, Yves Meyer
We consider Delone point patterns with self-similarity. Under mild conditions, the similarity factor is a Pisot number if and only if the pattern is uniformly discrete. The classic…
Quasicrystal model sets from overlapping self-similar attractors
Christoph Bandt, Yves Meyer
We give a simple computational approach to mathematical quasicrystals, combining cut-and-project methods with self-similarity. Starting with a Pisot unit and an iterated functi…
Elementary fractal geometry. 6. The dynamical interior of self-similar sets
Christoph Bandt
On the one hand, the dynamical interior of a self-similar set with open set condition is the complement of the dynamical boundary. On the other hand, the dynamical interior is the…
Elementary fractal geometry. 5. Weak separation is strong separation
Christoph Bandt, Michael F. Barnsley
For self-similar sets, there are two important separation properties: the open set condition and the weak separation condition introduced by Zerner, which may be replaced by the fo…
Elementary fractal geometry. 4. Automata-generated topological spaces
Christoph Bandt
Finite automata were used to determine multiple addresses in number systems and to find topological properties of self-affine tiles and finite type fractals. We join these two line…