15. September 2025

Random square tiling

A random periodic square tiling of the plane with 4000 squares.
Figure A random periodic square tiling of the plane with 4000 squares.
Figure Another random periodic square tiling of the plane with 4000 squares.
Figure Another random periodic square tiling of the plane with 4000 squares.

Interactive app

An interactive version of the random square tiling is available as a live javascript app.

Videos

Video A compilation video of several rotating square tilings of the plane.
Video Another compilation of square tilings, but this time the squares themselves are rotating.

References

[1] Brooks, Rowland L., Cedric AB Smith, Arthur H. Stone, and William T. Tutte. “The dissection of rectangles into squares.” In Classic Papers in Combinatorics, pp. 88-116. Boston, MA: Birkhäuser Boston, 1940.

[2] Georgakopoulos, Agelos, and Christoforos Panagiotis. “Convergence of square tilings to the Riemann map.” arXiv preprint arXiv:1910.06886 (2019).

[3] Addario-Berry, Louigi, and Nicholas Leavitt. “Random infinite squarings of rectangles.” (2016): 596-611.

[4] Bertacco, Federico, Ewain Gwynne, and Scott Sheffield. “Scaling limits of planar maps under the Smith embedding.” The Annals of Probability 53, no. 3 (2025): 1138-1196.

Latest Posts