hypertiling

hypertiling is a high-performance Python library for the generation and visualization of regular hyperbolic lattices embedded in the Poincare 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.

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Installation

hypertiling is available in the PyPI package index and can be installed using

$ pip install hypertiling

The package can also be locally installed from our public git repository via

$ git clone https://git.physik.uni-wuerzburg.de/hypertiling/hypertiling
$ pip install .

Usage

In order to use the package, in Python do the following import

from hypertiling import HyperbolicTiling

Set parameters, initialize and generate the tiling

p = 7
q = 3
nlayers = 5

T = HyperbolicTiling(p,q,nlayers)

Further examples are available in our documentation and Jupyter demo notebooks.

Authors

This project is developed at:
Institute for Theoretical Physics and Astrophysics
University of Wuerzburg

Citation

If you use hypertiling, we encourage you to cite or reference this work as you would any other scientific research. The package is a result of a huge amount of time and effort invested by the authors. Citing us allows us to measure the impact of the research and encourages others to use the library.

Cite us:

Manuel Schrauth, Yanick Thurn, Florian Goth, Jefferson S.E. Portela, Dietmar Herdt and Felix Dusel. (2023). The hypertiling project. Zenodo. https://doi.org/10.5281/zenodo.7559393

Examples

In this animation we simulate a classical scalar field Hamiltonian on two different lattice structures. The setting can be interpreted as a simple model for magnetic behaviour in a solid crystal structure. In particular, couplings between adjacent cells (“spins”) are adjusted in a way which energetically favors anti-parallel local alignment. Both systems are initiated in a random “hot” configuration of positive (red) and negative (green) field values, which - in the magnetic picture - can be interpreted as uniaxial spins pointing upwards or downwards, respectively. The animation demonstrates the effect of a Metropolis algorithm being repeatedly applied - until the system reaches thermal equilibrium.

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License

Every part of hypertiling is available under the MIT license.