15. December 2025

Random self-overlapping disks

A uniform random flat quadrangulation of perimeter 15170 embedded in three-dimensional space.
Figure A uniform random flat quadrangulation of perimeter 15170 embedded in three-dimensional space.
Figure A uniform random flat quadrangulation of perimeter 4000
Figure A uniform random flat quadrangulation of perimeter 14698
Figure A uniform random flat quadrangulation of perimeter 12134
Video A rotating version of the cover image: a flat quadrangulation of perimeter 15170.
Video A rotating version of the image above.
Video A uniform random flat quadrangulation of perimeter 5000.

References

[1] Ferrari, Frank. “Jackiw-Teitelboim gravity, random disks of constant curvature, self-overlapping curves, and Liouville CFT 1.” Physical Review D 111, no. 6 (2025): L061901.

[2] Ferrari, Frank. “Random disks of constant curvature: the lattice story.” Physical Review D 113, no. 2 (2026): 026012.

[3] Budd, Timothy. “Discrete flat disks: rigid quadrangulations.” arXiv preprint arXiv:2509.24785 (2025).

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