A Family of Non-Periodic Tilings, Describable Using Elementary Tools and Exhibiting a New Kind of Structural Regularity

TL;DR

This paper introduces a new family of non-periodic tilings characterized by a novel form of structural regularity called modulo-staggered rotational symmetry, constructed using simple mathematical tools.

Contribution

It presents a self-contained construction of non-periodic tilings with a unique regularity, expanding the understanding of tiling symmetries without relying on existing theories.

Findings

Tilings exhibit modulo-staggered rotational symmetry

Construction uses elementary tools like modular arithmetic and vector geometry

Provides a new perspective on non-periodic tiling regularities

Abstract

We present a construction of a family of non-periodic tilings using elementary tools such as modular arithmetic and vector geometry. These tilings exhibit a distinct type of structural regularity, which we term modulo-staggered rotational symmetry. The construction is self-contained and does not rely on previous tiling theories or systems.