3D surface plot of the height function for a uniformly random domino tiling of the Aztec diamond, colored by domino type (blue, green, red, yellow). Demonstrates the arctic circle phenomenon separating frozen and disordered regions. Set diamond order n up to 320, toggle demo rotation mode, and pan 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.
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)