This simulation demonstrates random domino tilings of an Aztec diamond, which is a diamond-shaped union of unit squares. The simulation uses a measure with $3\times 3$ periodic weights, extending the work by Chhita and Johansson on 2×2 periodic weights.
The weight assignment uses a full 3×3 block pattern with 9 different weights:
[w₁ w₂ w₃]
[w₄ w₅ w₆]
[w₇ w₈ w₉]
Each position in the 3×3 grid can have its own weight parameter, allowing for complex periodic patterns. The simulation uses the shuffling algorithm. The original python code was created by Sunil Chhita; this version is adapted for JS + WebAssembly. Visualization is done using D3.js.
The sampler works in your browser. Up to $n \sim 120$ it works in reasonable time, but for larger $n$ it may take a while. I set the upper bound at $n=300$ to avoid freezing your browser.
Link to code
(This simulation is interactive, written in JavaScript; see the source code of this page at the link)
Link to code
(C++ code for the simulation)