HYPERTILING -- a high performance Python library for the generation and visualization of hyperbolic lattices

TL;DR

HYPERTILING is a high-performance Python library that efficiently generates and visualizes large hyperbolic lattices, supporting advanced manipulation, plotting, and animation for research and educational purposes.

Contribution

The paper introduces HYPERTILING, a novel Python library that enables fast creation and visualization of large hyperbolic lattices with advanced features, filling a gap in existing tools.

Findings

Lattices with millions of vertices generated in minutes

Supports dynamic manipulation and refinements of hyperbolic graphs

Provides comprehensive visualization and animation capabilities

Abstract

HYPERTILING is a high-performance Python library for the generation and visualization of regular hyperbolic lattices embedded in the Poincar\'e disk model. Using highly optimized, efficient algorithms, hyperbolic tilings with millions of vertices can be created in a matter of minutes on a single workstation computer. Facilities including computation of adjacent vertices, dynamic lattice manipulation, refinements, as well as powerful plotting and animation capabilities are provided to support advanced uses of hyperbolic graphs. In this manuscript, we present a comprehensive exploration of the package, encompassing its mathematical foundations, usage examples, applications, and a detailed description of its implementation.