hypertiling is a high-performance Python 3 library for the generation of regular hyperbolic tilings embedded in the Poincaré disk model. Using efficient algorithms and the CPU/SIMD optimization provided by numpy, hyperbolic tilings with hundreds of millions of vertices can be created in a matter of minutes on a single computer. Facilities including optimized search algorithms for adjacent vertices and powerful plotting and animation capabilities are provided to support scientific and other advanced uses of the graphs.
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.