Domino Shuffling Algorithm on Aztec Diamond

This is an animated generation of a Random Domino Tiling on a Aztec Diamond.

The algorithm that produces this Random Domino Tiling is called Domino Shuffling and it is uniformly sampling a domino tiling. The surprising effect is that, a uniformly sampled domino tiling tends to "froze" on corners, outside of a circle called Arctic Circle.

References

• Elkies, N., Kuperberg, G., Larsen, M., & Propp, J. (1992). Alternating sign matrices and domino tilings. arXiv. https://doi.org/10.48550/ARXIV.MATH/9201305
• Janvresse, É., Rue, T. de la, & Velenik, Y. (2006). A Note on Domino Shuffling. In The Electronic Journal of Combinatorics (Vol. 13, Issue 1). The Electronic Journal of Combinatorics. https://doi.org/10.37236/1056
• Jockusch, W., Propp, J., & Shor, P. (1998). Random Domino Tilings and the Arctic Circle Theorem (Version 1). arXiv. https://doi.org/10.48550/ARXIV.MATH/9801068

Algorithm is implemented in javascript by tada-s. Visualization and animation is done using D3.js.