Domino tilings of the Aztec diamond with 2x2 periodic weights     domino-tilings

Displays a colored domino tiling of an Aztec diamond with 2-by-2 periodic weights. Four colors encode domino orientations, and the weight parameters a, b shape arctic curves separating frozen corners from disordered regions. Controls set the diamond size, weight parameters, and grayscale mode.

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 $2\times 2$ periodic weights, as in the paper by Chhita and Johansson. 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.

Update 2025-04-14: TikZ Code Generation

You can now get a TikZ code for the sampled Aztec diamond directly by clicking the button below. This feature supports dominoes with appropriate coloring.

Skip to simulation canvas

code

• 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)

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