Inductive Rotation Tilings

TL;DR

This paper introduces a novel method for creating aperiodic tilings, demonstrating their properties such as nonperiodicity, aperiodicity, and pure point diffraction, with detailed analysis of a specific tiling and its hull.

Contribution

It presents a new construction method for aperiodic tilings and analyzes their mathematical properties, including substitution rules and diffraction characteristics.

Findings

The tilings have substitution rules.

They are nonperiodic and aperiodic.

They exhibit pure point diffraction.

Abstract

A new method for constructing aperiodic tilings is presented. The method is illustrated by constructing a particular tiling and its hull. The properties of this tiling and the hull are studied. In particular it is shown that these tilings have a substitution rule, that they are nonperiodic, aperiodic, limitperiodic and pure point diffractive.