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:

• Perfect t‑Embeddings of Uniformly Weighted Aztec Diamonds and Tower Graphs
  Tomas Berggren, Matthew Nicoletti, Marianna Russkikh (2023, IMRN)
  DOI:10.1093/imrn/rnad299
• Bipartite Dimer Model: Perfect t‑Embeddings and Lorentz‑minimal Surfaces
  Dmitry Chelkak, Benoît Laslier, Marianna Russkikh (2021)
  arXiv:2109.06272
• Fluctuations in the Aztec Diamonds via a Lorentz‑minimal Surface
  Dmitry Chelkak, Sanjay Ramassamy (2020)
  arXiv:2002.07540

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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))