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.
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.
Every part of hypertiling is available under the MIT license.