Shuffling Algorithm for Domino Tilings in Terms of Particles domino-tilings

Leonid Petrov

Simulation Info

Shuffling Algorithm for Domino Tilings in Terms of Particles domino-tilings

Leonid Petrov

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Target n:

Speed: n=0

Granular steps Rotate 45° Particles Show λ,μ

About the Algorithm

Forward EKLP Shuffling builds random tilings of Aztec diamonds via the map A_n → A_n+1:

Delete bad blocks: Remove colliding pairs: N-S (N bottom, S top) and E-W (E left, W right)
Slide: Each domino slides one unit in its direction (N↑, S↓, E→, W←)
Fill holes: Fill each empty 2×2 block with a random domino pair

Enable "Granular steps" to see each phase separately. Bad blocks are highlighted in red before deletion.

References:

arXiv:math/9201305 — Elkies, Kuperberg, Larsen, Propp (EKLP shuffling)

code

(note: parameters in the code might differ from the ones in simulation results below)

Link to code (Pure JavaScript implementation of EKLP shuffling)

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