Two random tilings make these loops

About this video

Lay two random domino tilings on top of each other, delete every domino they share, and only loops are left.

Here two independent uniformly random tilings of a 127 x 207 Temperleyan rectangle, one cyan and one gold, leave 1,721 loops. The longest loop is traced, then all of them ring from smallest to largest. Each domino plucks a note as it lands: higher on screen, higher note. Small loops ring high and big loops ring low.

OpenAI, ChatGPT's creator, reports a proof that the complete double-dimer loop ensemble for the Temperleyan square lattice in the upper half-plane converges to nested CLE4. This is a source-reported result, not independently reviewed or proof-audited in this production, and the public ChatGPT product is not claimed to have proved it. The animation shows one finite random sample as an illustration, not the proof; the paper works in the half-plane scaling limit.

Source manuscript:
The Curve Scaling Limit of Half-Plane Double Dimers
github.com/openai/math/blob/main/preprints/The-curve-scaling-…

Corrections and withdrawals: github.com/openai/math/blob/main/history.md

Sound and visuals: original code-generated synthesis and animation. No third-party samples or compositions. Native 2160x3840 at 60 fps.

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