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math.DS2026
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…
math.MG2026
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…