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