hypertiling is a Python 3 library for fast generation of regular 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 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) 
T.generate()

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

Authors

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

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

Examples

Simulation of a Ising-like Boltzmann spin model on a hyperbolic (7,3) tiling at low temperature. One readily recognizes a number of magnetic domains of opposite spin orientation (red/blue areas). The domain walls are approximately given by arcs of Euclidean circles contained within the disk and orthogonal to its boundary. These arcs represent straight lines in the Poincare disk representation of the hyperbolic plane.

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License

Every part of hypertiling is available under the MIT license.