3D Visualization of 3x3 periodic Domino Tilings of the Aztec Diamond     domino-tilings

Leonid Petrov


Simulation Info

3D Visualization of 3x3 periodic Domino Tilings of the Aztec Diamond     domino-tilings

Leonid Petrov

3D surface plot of the height function for a domino tiling of the Aztec diamond with 3-by-3 periodic edge weights. Nine adjustable weight parameters shape frozen and liquid regions, producing non-circular arctic curves. Set diamond order n up to 320, tune the weight grid, toggle demo rotation, and navigate the camera with arrow buttons or keyboard.

This simulation displays random domino tilings of an Aztec diamond using its three-dimensional height function. The visualization is inspired by Alexei and Matvey Borodin’s visualizations. Caution: large values of $n$ may take a while to sample. If $n\le 100$, it should be reasonably fast.

3×3 Periodic Weights


code

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

Dear colleagues:

Feel free to use code (unless otherwise specified next to the corresponding link), data, and visualizations to illustrate your research in talks and papers, with attribution (CC BY-SA 4.0 (opens in new tab)). Some images are available in very high resolution upon request. I can also produce other simulations upon request - email me at lenia.petrov@gmail.com
This material is based upon work supported by the National Science Foundation under Grant DMS-2153869