Domino tilings of the Aztec diamond     domino-tilings

Displays a colored grid of dominoes tiling an Aztec diamond shape, where four colors indicate domino orientations. The arctic circle separates frozen corner regions from a disordered interior. Controls set the diamond size and toggle between domino, dimer, path, and height function views.

This simulation demonstrates random domino tilings of an Aztec diamond, which is a diamond-shaped union of unit squares. The simulation uses a uniform measure to generate random tilings via 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 $n=400$ 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 and nonintersecting paths only.

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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