Interactive 3D visualization of lozenge tilings with q-volume and q-Racah weights. The height function is displayed as a three-dimensional surface. Supports Glauber dynamics and coupling from the past sampling with uniform, q-volume, and q-Racah weighting options.
About this simulation
This simulation demonstrates 3D lozenge tilings using a WASM/JS port of a program by Vadim Gorin.
The simulation generates lozenge tilings of a hexagon with sides $N$, $S$, and $T-S$ under the $q^{-volume}$ measure, including support for the imaginary q-Racah case introduced by Borodin, Gorin, and Rains (2009).
The sampler works entirely in your browser using WebAssembly. This version provides both 2D and 3D visualization modes with full S→S±1 operator functionality for all supported polynomial families.
The sampler works entirely in your browser using WebAssembly. This version provides both 2D and 3D visualization modes with full S→S±1 operator functionality for all supported polynomial families.
Keyboard Shortcuts
Animation
| A | S → S+r |
| Z | S → S-r |
| S | S → S+r → S-r |
| X | S → S-r → S+r |
View
| V | Toggle 2D/3D view |
| R | Reset camera (3D only) |
| Shift+Drag | Pan camera (3D only) |
Colors
| C | Next color palette |
| Shift+C | Previous color palette |
| P | Permute colors |
| B | Cycle border style |
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)