Constructing quasicrystalline lattices

TL;DR

This paper introduces a novel method for constructing quasicrystalline lattices using Landau crystallization theory, avoiding traditional acceptance domains by employing simple local rules based on real-space order.

Contribution

It presents a new approach to quasicrystal lattice construction that simplifies the process by eliminating the need for acceptance domains, relying instead on local order rules.

Findings

The method successfully constructs quasicrystalline lattices.

It simplifies the process compared to traditional cut and projection methods.

The approach is based on Landau crystallization theory.

Abstract

A new method to construct quasicrystalline lattices is proposed. It is based on Landau crystallization theory. Like well-known cut and projection methods our approach deals with N dimensional crystallography, but we don't need any conception similar to an acceptance domain or atomic surfaces. The selection of nodes, included into the lattice, is based on simple rules provided their local order in a real space.