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.

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Current Configuration

N = 40 T = 80 S = 10 q = 1

Color Legend

Up Down Horizontal Border UVA

Keyboard Shortcuts

Keyboard shortcuts:
A: S → S+r
Z: S → S-r
S: S → S+r → S-r
X: S → S-r → S+r
V: Toggle 2D/3D view
C: Next color palette
Shift+C: Previous color palette
P: Permute colors (cycle through 6 permutations)
B: Change border style (thin/medium/thick/ultra thick)
R: Reset camera (3D view only)
Shift+Drag: Pan camera (3D view only)

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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)

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