Do you remember the Eames Powers of Ten film? It is a classic short film that explores the relative scale of the universe in factors of ten. I’ve always loved the way it visualizes the vastness of space and the minuteness of the microscopic world.
The original film was made in 1977 by Charles and Ray Eames, and it has inspired many to think about scale in a new way. Using Three.js, a popular JavaScript library for 3D graphics, I decided to use LLMs to recreate the Powers of Ten experience in a web browser. This allows users to interactively explore the universe from the largest scales down to the smallest.
The 1977 film crosses forty-one orders of magnitude in nine minutes, from a picnic
blanket out to the superclusters and back down into a carbon nucleus. That span is
the entire engineering problem. A float32 carries about seven decimal digits; no
scene graph holds 10⁴¹ in absolute coordinates.
So the camera is bolted to the origin and never moves. Everything is a function of
one scalar — s, the log of how many metres the frame spans. Content is authored
per decade in normalised units and placed into the scene scaled by 10^(level - s).
Only about three decades are ever live at once, which keeps that exponent inside
±1.5. Every number the GPU sees is ordinary, whether you are looking at quarks or at
superclusters.
10⁰ m. The nested squares are the film’s signature and they fall straight out of the maths: a square denoting 10^L metres occupies 10^(L−s) of the frame. The grid is diagnostic content — one cell of each decade is exactly the next decade’s full extent, so if the scaling were wrong by a hair, nothing would nest.
One thing took me three attempts to get right: the square defines the scale, not the camera. My first version drew the square at 46% of a frame it claimed was the full field of view. The two disagreed by a factor of 2.15, which made the HUD a decoration rather than an instrument.
Take a look at the demo here: Powers of Ten in Three.js
Every catalogue draws you its own edge
The star field comes from the HYG catalogue — 108,401 real stars, Sirius where Sirius actually is. It looks superb at 10¹⁸ m and becomes a lie about two decades later.
HYG is magnitude-limited, so how deep it is complete depends on how far away you look. Measured in shells, its apparent stellar density falls by a factor of 26,000 between the solar neighbourhood and 900 parsecs, while the real galactic disk is roughly flat over that range. Viewed from a receding camera that reads as a dense knot of stars around the Sun thinning into nothing: a picture of the survey, not of the sky.
10¹⁸ m. Real stars, with real colours derived from their B−V indices.
10²¹ m. A raymarched emission-absorption volume. The bulge sits off-centre because the Sun does — every band is heliocentric, since the piece holds its starting point at frame centre.
The same thing happens again two decades up. The galaxy catalogue reaches 3 megaparsecs; by 10²³ m the viewpoint is 9.8 Mpc out, three times past the far edge of the data, and the galaxies cover 0.01% of the frame. Both bands now stop where their data stops and hand over to a procedural field.
A subtler version of the same bug nearly got past me. Star brightness is normalised against the camera’s own distance so the field does not fade out as the viewpoint recedes. But every field here is bounded while the viewpoint keeps going — so past the edge of the content, the exposure was compensating for distance the content no longer spanned, collapsing what remained into a bright knot and pumping it brighter the further away it got.
| Star band coverage, 10¹⁸ → 10²⁰ | Result |
|---|---|
| Exposure tracking the camera past the data | 0.47 → 39.5 |
| Exposure pinned to the band’s own decades | 0.57 → 0.02 |
Coverage of 39.5 means the ink laid down was thirty-nine times the area of the frame. It was a solid white wash, and I had looked at it several times without registering that anything was wrong.
Everything below a micron is free
The journey inward costs nothing to store. Hydrogen-like electron orbitals have a closed form, so |ψ|² is a two-line expression and the shapes are the real ones. Cells are a jittered lattice. DNA is a distance function. No textures, no downloads, no licences.
10⁻⁴ m. Cells on a jittered lattice, each with a membrane shell and an offset nucleus.
10⁻⁸ m. B-form DNA: 2 nm across, 3.4 nm per turn, ten base pairs to the turn.
That helix took two tries. First it rendered as pure colour noise: a strand is 0.034 local units thick and the ray marcher was stepping 0.17 at a time, walking straight past it, with the per-pixel jitter that normally hides banding turning the misses into static. Then it rendered as a disc — because I had run the helix along the z axis, which is the axis the camera looks down.
Measure the picture, don’t look at it
Nearly every real bug in this project was found by rendering to a buffer and computing a number, and several of them had survived my looking directly at them.
- A galaxy field at identical coverage looked like porridge. The number that explained it was ink per star: 122 px² against the catalogue’s 23. Half as many stars at four times the area gives the same total and reads as mush.
- A “modest” 12% giant-star fraction made giants 89% of everything large enough to resolve, because luminous stars are only 0.4% of the luminosity function. The field came out uniformly orange.
- Twice I was convinced the galaxy was rendering ten times too small. Measuring the radial profile showed the frame spanned exactly the predicted 3.5 kpc. My expectation was wrong, not the code.
- The audio layer weights summed to 1, which I assumed meant a level mix. Rendered offline, it climbed 18 dB from one end of the journey to the other, because shimmer runs eight times quieter than filtered noise.
| Base image brightness, 800px → 200px tall | Result |
|---|---|
| Point size with a fixed pixel floor | 30 → 179 |
| Point size scaled against the viewport | 22 → 18 |
That last one I found while preparing to deploy, in a test that simulated serving
the page from a subdirectory. The deployment was fine. The test caught something
else entirely: the image depended on window size, because gl_PointSize is in
pixels with a one-pixel floor, so the same 108,401 stars cover a far larger fraction
of a small canvas than a large one.
Ten layers on the same window function
The score is synthesised — no samples, nothing anyone owns, zero bytes. Ten layers tile the full range and are mixed through the identical window function the visuals cross-fade on, so a sound layer fades on exactly the curve its matching picture does.
A drone tracks s directly and falls five octaves, 440 Hz at the quantum end to
13.75 Hz at the cosmic one. Measured across the journey, the spectral centroid drops
from 4,215 Hz to 64 Hz: the piece literally descends in pitch as the frame opens up.
Twenty-three of forty-one
The whole inward journey is built, and everything from the local stars outward. What is missing is the stretch from the picnic blanket to the stars — 10⁰ to 10¹⁶ — and it is missing for an honest reason: it needs photographs, orthoimagery and ephemerides rather than shaders. That was always the Eameses’ real work. Forty distinct plates, hand-made.
One decade is deliberately left as a diagnostic grid. At 10⁻¹² m you are between the electron cloud and the nucleus, and there is genuinely nothing there. Faking something would be worse than admitting it.
Star data: HYG Database (astronexus), CC BY-SA 4.0. Galaxy data: McConnachie 2012, AJ 144, 4. Powers of Ten (1977) is © the Eames Office. This is an homage with its own art, score and text.