This page is an interactive visualization of the two canonical embeddings (T and O) of the Aztec‑diamond graph with uniform ($a=1$) or $2\times 2$ periodic edge weights depending on a parameter $a\ne 1$. In the T‑embedding, every face is a quadrilateral with the same cyclic product of edge lengths as in the original Aztec diamond graph. The companion O‑embedding in 2D represents the origami folding of the T-embedding. The 3D view lifts the T‑coordinates by $\mathrm{Im}(O)$.

The 2D T-embedding can be exported in TikZ format using the Export TikZ button below.

Large sizes (n > 100) are computation‑intensive; the code runs entirely in your browser, therefore patience is advised on mobile.

Selected references:

1. T. Berggren, M. Nicoletti, M. Russkikh, "Perfect t‑Embeddings of Uniformly Weighted Aztec Diamonds and Tower Graphs," IMRN, 2023 (doi:10.1093/imrn/rnad299).
2. D. Chelkak, B. Laslier, M. Russkikh, "Bipartite Dimer Model: Perfect t‑Embeddings and Lorentz‑Minimal Surfaces," arXiv:2109.06272, 2021.
3. D. Chelkak, S. Ramassamy, "Fluctuations in the Aztec Diamonds via a Lorentz‑Minimal Surface," arXiv:2002.07540, 2020.

Last updated: 2025-04-20

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). 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