88 citations · 1.6k across the 104 of their papers we have counts for
104 papers
Forward limit sets of semigroups of substitutions
Ibai Aedo, Uwe Grimm, Ian Short
We introduce the forward limit set of a semigroup generated by a family of substitutions of a finite alphabet, which typically coincides with the set of all possible s-adic…
Monochromatic arithmetic progressions in automatic sequences with group structure
Ibai Aedo, Uwe Grimm, Neil Mañibo +2
We determine asymptotic growth rates for lengths of monochromatic arithmetic progressions in certain automatic sequences. In particular, we look at (one-sided) fixed points of aper…
Inflation versus projection sets in aperiodic systems: The role of the window in averaging and diffraction
Michael Baake, Uwe Grimm
Tilings based on the cut and project method are key model systems for the description of aperiodic solids. Typically, quantities of interest in crystallography involve averaging ov…
Three variations on a theme by Fibonacci
Michael Baake, Natalie Priebe Frank, Uwe Grimm
Several variants of the classic Fibonacci inflation tiling are considered in an illustrative fashion, in one and in two dimensions, with an eye on changes or robustness of diffract…
Fourier transform of Rauzy fractals and point spectrum of 1D Pisot inflation tilings
Michael Baake, Uwe Grimm
Primitive inflation tilings of the real line with finitely many tiles of natural length and a Pisot--Vijayaraghavan unit as inflation factor are considered. We present an approach…
Quasicrystals
Uwe Grimm, Peter Kramer
Mathematicians have been interested in non-periodic tilings of space for decades; however, it was the unexpected discovery of non-periodically ordered structures in intermetallic a…