Interactive 3D surface showing the t-embedding of an Aztec diamond graph with doubly periodic weights. Height is given by the origami map imaginary part. Adjust diamond size n and weight parameter a; orbit, pan, and zoom the 3D view with mouse or arrow keys. Demo mode auto-rotates.
An illustration of the T-embedding of the Aztec diamond graph (parameter \(n\)), with 3D height given by the imaginary part of the O-embedding. The \((x,y)\) coordinates come from \(\mathrm{Re}(T), -\mathrm{Im}(T)\), and the \(z\) coordinate is \(\mathrm{Im}(O)\).
Some references:
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Perfect t‑Embeddings of Uniformly Weighted Aztec Diamonds and Tower Graphs
Tomas Berggren, Matthew Nicoletti, Marianna Russkikh (2023, IMRN)
DOI:10.1093/imrn/rnad299 (opens in new tab) -
Bipartite Dimer Model: Perfect t‑Embeddings and Lorentz‑minimal Surfaces
Dmitry Chelkak, Benoît Laslier, Marianna Russkikh (2021)
arXiv:2109.06272 (opens in new tab) -
Fluctuations in the Aztec Diamonds via a Lorentz‑minimal Surface
Dmitry Chelkak, Sanjay Ramassamy (2020)
arXiv:2002.07540 (opens in new tab)
code
(note: parameters in the code might differ from the ones in simulation results below)-
Link to code(Interactive 3D T-embedding; see the source code of this page at the link) -
Link to code(C++ code for the simulation with tunable scale parameter a (3D version))