Tegula -- exploring a galaxy of two-dimensional periodic tilings

TL;DR

This paper introduces Tegula, a software tool and database that systematically explores and visualizes a vast collection of 2D periodic tilings with Dress complexity up to 24, aiding research in art, construction, and crystallography.

Contribution

It presents a comprehensive database of 2.4 billion periodic tilings and a new software tool, Tegula, for searching and visualizing these tilings, expanding the scope of combinatorial tiling exploration.

Findings

Database of 2.4 billion tilings available for research.

Tegula software enables efficient search and visualization.

Open source access promotes further exploration.

Abstract

Periodic tilings play a role in the decorative arts, in construction and in crystal structures. Combinatorial tiling theory allows the systematic generation, visualization and exploration of such tilings of the plane, sphere and hyperbolic plane, using advanced algorithms and software.Here we present a "galaxy" of tilings that consists of the set of all 2.4 billion different types of periodic tilings that have Dress complexity up to 24. We make these available in a database and provide a new program called Tegula that can be used to search and visualize such tilings. Availability: All tilings and software and are open source and available here: https://ab.inf.uni-tuebingen.de/software/tegula.