Shuffling algorithm for q-volume lozenge tilings of the hexagon lozenge-tilings
Vadim Gorin (original code); Leonid Petrov (porting)
Colorful lozenge tiling of a hexagon under the q-to-the-volume probability measure, generated by Gorin's shuffling algorithm. Three rhombus orientations tile the hexagonal region with parameters N, T, S controlling side lengths and q weighting the volume. Controls adjust parameters and palette; animation steps shuffle the tiling forward and back.
About this simulation
This simulation demonstrates 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.
The sampler works entirely in your browser using WebAssembly.
The sampler works entirely in your browser using WebAssembly.
Parameters
Animation Controls
More Options
View Controls
Styling Controls
Custom Color Palettes
Export
Current Configuration
N = 20
T = 30
S = 25
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
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)
A: S → S+r
Z: S → S-r
S: S → S+r → S-r
X: S → S-r → S+r
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)
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)