hypertiling is a high-performance Python 3 library for the generation and visualization of hyperbolic tilings, embedded in the Poincaré disk model. Using efficient, precise and robust algorithms, isometric lattices with millions of polygons can be created in a matter of minutes on a single computer and are ready to be used for all sorts of scientific as well as artistic purposes.

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Installation and Usage

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

$ pip install hypertiling

The package can also be locally installed. First download or clone the package from our public git repository, using

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

Now execute

$ pip install .

in the package’s root directory to install the package in-place.

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

• Manuel Schrauth
  mschrauth@physik.uni-wuerzburg.de
• Felix Dusel
• Yanick Thurn
• Florian Goth
• Dietmar Herdt
• Jefferson S. E. Portela

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

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.