Lattice Dimers
This is the site of Lattice Dimers, a research project that counts the ways to cover a board with pieces of two cells. A domino covers two cells sharing a side, a domicule two cells sharing a side or only a corner. A chessboard has 12,988,816 domino tilings (OEIS A004003) and 3,263,262,629,905 domicule tilings (OEIS A239273). The code, the data and the OEIS entries of the project are in the repository.
- Gallery: numbers the tilings of a rectangle, a cylinder or a torus and draws any one of them; boards too large to number are sampled.
- Benchmarks: the exact counts and the running times of the solvers in Rust, Python and JavaScript, on boards up to 20 × 20.
- Notebooks, in the menu: the methods for dominoes, domicules and the triangular lattice, with code that runs whenever the site is built.
- Research: the entropy per site of domicule tilings, estimated at s = 0.5655119110413253 ± 6·10⁻¹⁶ and proved to lie between 0.545343749727 and 0.582767477484, with the paper and its companion note.
A dash under BigInt is a board it was not measured on; the dash's tooltip says why.
A dash under BigInt is a board it was not measured on; the dash's tooltip says why.
A dash under BigInt is a board it was not measured on; the dash's tooltip says why.
A dash under BigInt is a board it was not measured on; the dash's tooltip says why.
A dash under BigInt is a board it was not measured on; the dash's tooltip says why.
These solvers have no benchmark run yet.
A dash under BigInt is a board it was not measured on; the dash's tooltip says why.
A dash under BigInt is a board it was not measured on; the dash's tooltip says why.
These solvers have no benchmark run yet.
Mean time of the count each solver reports with --time. The tooltip of a time gives the whole process,
start-up included.
Results: benchmarks/results/ee071e57836d-node26.11.1-python3.14.5-rust1.99.1.