STUDY #14 · 2026 · IN OBSERVATION

Caustics

A model-driven visual study of light focused by a waving water surface.

MOVING IMAGE — THE FOCUSING ARC d̃ 0.45 → 1.15 → 2.6 → 0.45 · noon pool

WHAT IS THIS

Caustics are the bright dancing lines on the bottom of a pool. A waving water surface acts as a field of lenses: refracted sunlight folds over itself, and where the ray map folds, light piles up into a luminous web. Catastrophe optics classifies the stable singularities of such maps — smooth folds and pointed cusps are the only letters, whatever the sea happens to look like. Where study #06 added waves as phases, here the light is bent as rays — the web is the fold of a map, not an interference pattern.

This study implements the ray map directly: a sum-of-sines water surface (deep-water dispersion ω = √(gk)) refracts millions of photons by vector Snell's law onto the floor plane. It runs in real time on the GPU, and the depth of the floor — measured in focal lengths of the surface — is the single dial that moves the picture through its regimes.

the net — the sharpest single web, just past focus d̃ 1.15 · net_s7 · sun 0° · noon pool · 4.2M photons

Motif caustics / catastrophe optics / refraction, fold and cusp

Method A small simulator was generated and modified with AI assistance, then ported to a real-time GPU (GLSL) renderer. The visual output was selected through parameter exploration.

Observation A single dimensionless depth (D/z*) rules the regime — soft cells before focus, one sharpest net at focus, nets folded over nets beyond it. Fold lines and cusps are the only letters the web is written with, and the rainbow edge on every line is real dispersion, not post-processing.

Reference M. V. Berry and C. Upstill, "Catastrophe optics: morphologies of caustics and their diffraction patterns," Progress in Optics, vol.18, 257-346 (1980).

Tools Python / NumPy / three.js / React / GLSL / ffmpeg / AI coding assistant

Year 2026

This is not a scientific simulation result, but a visual interpretation of the phenomenon.

PARAMETERS EXPLORED

param meaning effect on the image

d̃ = D/z* the floor depth, measured in focal lengths of the surface the one dial: <1 soft blur ⇄ ≈1 the sharpest single net ⇄ >2 nets folded over nets

λₚ the dominant wavelength of the surface the cell size of the web — 0.25 m dense sparkle to 0.9 m broad plates

anisotropy how strongly the waves share one direction 0 gives a cellular net ⇄ 0.95 gives flowing braids

sun tilt the sun's inclination stretches the net and skews the cusps — the drama axis

dispersion per-channel refractive indices (R/G/B) the width of the rainbow fringe on every bright line — real dispersion

absorption Beer-Lambert absorption of water the palette of depth — red is eaten first, teal and blue remain

Each image below records its exact parameter set.

SELECTED STILLS — 5

the net — the sharpest single web d̃ 1.15 · net_s7 · noon pool

sparkle — a short chop d̃ 1.0 · sparkle_s11 · noon pool

a swell — braids drawn by one long wave train d̃ 1.0 · swell_s11 · sun 15° · lagoon

cusp drama by a low moon d̃ 1.3 · sun 35° · dispersion 1.2 · moonlit

folded nets — the web laid over itself d̃ 2.5 · net_s7 · deep sea

PROCESS — PARAMETER SWEEPS

The focusing arc as a contact sheet — the same surface, the floor diving through the regimes: soft cells above focus, the single sharpest net at d̃ ≈ 1, folded nets beyond.

the depth sweep d̃ 0.45 → 1.15 → 2.6 · net_s7

SIGNATURE — THE DEPTH GAUGE

One dial rules the picture — depth, measured in focal lengths.

A water surface has a focal length, like any lens. Measure the floor's depth in that unit — d̃ = D/z* — and every random sea behaves the same way: blur above focus, one sharpest net at d̃ ≈ 1, and past it the web folds over itself again and again. The hero film runs that dial up and down; the regimes arrive on schedule.

The letters never change — smooth folds and pointed cusps are the only stable singularities a ray map can carry. Any pool, any sea, any light: the same two letters, written at every depth.

how the web is written — the ray map folding into folds and cusps fold + cusp · the only stable letters · d̃ rules the regime

COLOUR = OPTICS

Nothing here is coloured by hand. The rainbow fringe on every bright line is dispersion: red, green and blue photons are refracted separately with the refractive indices of water (n ≈ 1.331 / 1.335 / 1.340), so blue focuses slightly shallower than red — the fringes are physics, not post-processing.

The palette of each piece is Beer-Lambert absorption: water eats red light first (α ≈ 0.34 /m at 650 nm vs 0.015 /m at 450 nm), so the deeper the floor, the more the ambient light sinks toward teal and blue. And the forms — smooth ribbons, and the pointed stars where they pinch — are the fold and cusp singularities of catastrophe optics.

depth as palette — six metres down, red long gone d̃ 2.5 · absorption 0.7 · deep sea

Refractive indices and absorption coefficients are artistic approximations of published values, not measurements.

REFERENCES

M. V. Berry and C. Upstill, "Catastrophe optics: morphologies of caustics and their diffraction patterns," Progress in Optics, vol.18, 257-346 (1980).