Distances in the latent space track distances between the decoded fields, so a field can be looked up by its embedding. Paint a field, pick a preset, or upload one, and find the most similar functions among 2,300 draws of 230 function families. Every function, yours included, is encoded as a single partition, so the bank holds only functions one partition reconstructs accurately.
Checking the server…230 families of smooth, low-frequency functions, 22 kinds of shape (waves, ripples, blobs, Chladni plates, vortices, saddles, stars, ...) under 12 mild transformations (symmetries, warps, windows, slopes, blurs, ...), ten random draws each. Every draw is encoded once, on a 64 × 64 grid as a single partition, and enters the bank only if that partition reconstructs it with a relative L2 error below 5%; its unit embedding is stored.
Your field is encoded the same way, as one partition on the same grid: one embedding for the whole field. Its reconstruction and error, next to the query, tell how well that embedding describes it.
The distance to every function of the bank is the chord distance between the two embeddings, dchord = 2 sin(θ/2) = |ζm − ζm′| / √dζ, as in the interpretability article: 0 for the same shape, 2 for opposite points of the sphere. The nearest are shown first.
Offsets and amplitudes live in the static frame, not in the embedding, so the search compares shapes: a field and a copy whose values are offset, or multiplied by a positive factor, are at distance zero.
One embedding holds the overall shape of a field, not its fine detail, so a match resembles the query as a whole; a family whose draws come up together is one the latent space groups. Click a match to search again from it.
Click a draw to search from it.