Domino tilings of the Aztec diamond domino-tilings

Leonid Petrov

Simulation Info

Domino tilings of the Aztec diamond domino-tilings

Leonid Petrov

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.

Aztec Diamond Order ($n\le 400$):

Show colors

Show checkerboard overlay

Show nonintersecting paths

Show dimers

Show height function

code

(note: parameters in the code might differ from the ones in simulation results below)

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)