Quasicrystals. The Technique for Constructing Quasiperiodic Structures

TL;DR

This paper introduces a new technique for constructing quasiperiodic structures, enabling the reconstruction of atom density distributions in quasicrystals, exemplified through the Penrose matching.

Contribution

It presents an algorithm for restoring atom density distributions in quasicrystals, demonstrated with the Penrose matching example.

Findings

Algorithm successfully reconstructs atom density in Penrose quasicrystal

Analytical model of Penrose quasicrystal provided

Method applicable to various quasiperiodic structures

Abstract

In this paper, a technique for constructing quasiperiodic structures is suggested, which allows one by the assigned matching to restore the atoms density distribution formula of a corresponding quasicrystal. The algorithm to restore the atom density distribution has been considered on the example of the Penrose matching. The analytical record of a Penrose quasicrystal is given.