Lattice-like properties of quasicrystal models with quadratic irrationalities (Q2711092)

Quasicrystals have been widely studied in physics and in mathematics arising as they do out of Penrose tiling. Model sets are developed for modeling physical quasicrystals and here the authors describe the possible values of the distances between adjacent points in the one-dimensional model sets based on quadratic unitary Pisot numbers. There are only three kinds of such distances in a particular model set, a fact related to the distribution of numbers \(n\theta\pmod 1\). Such model sets have self similarities. The aperiodicity has been used to improve the properties of random number generators.NEWLINENEWLINEFor the entire collection see [Zbl 0944.00084].