Discrete quasiperiodic sets with predefined covering cluster

TL;DR

This paper extends the strip projection method to higher-dimensional superspaces, enabling the efficient generation of complex discrete quasiperiodic sets with predefined local structures for applications in quasicrystal modeling.

Contribution

It introduces mathematical results that allow the use of the strip projection method in higher dimensions to produce more intricate quasiperiodic sets from covering clusters.

Findings

Hundreds of points generated in minutes using computer programs.

Method applicable to superspaces of dimension much higher than four to six.

Enables creation of quasiperiodic sets with complex local structures.

Abstract

Some of the most remarkable tilings and discrete quasiperiodic sets used in quasicrystal physics can be obtained by using strip projection method in a superspace of dimension four, five or six, and the projection of a unit hypercube as a window of selection. We present some mathematical results which allow one to use this very elegant method in superspaces of dimension much higher, and to generate discrete quasiperiodic sets with a more complicated local structure by starting from the corresponding covering cluster. Hundreds of points of these sets can be obtained in only a few minutes by using our computer programs.