The Address of Your Photograph
Fix a resolution and a colour depth and you have fixed a finite set of pictures. Yours is one of them.
- images this far out
- 1 — this one
- it now compresses to
- measuring…
- images at 64×64
- 10^29,592
Every bit costs the same amount of time as every other, so the stretch where nothing changes takes as long as it takes. Your image never leaves this tab.
The instruments
This image’s address
— at 64×64. In base 16,777,216 that address is the pixel list itself — one digit per pixel. The coordinate is the picture, under a fixed resolution, channel order, scan order and integer convention. Change any of those and it changes.
What the compression number is
One concrete code length under one serialization — deflate over an ordered byte stream, not an estimator of intrinsic complexity. It is an upper bound on the shortest description, never the shortest itself, which is not computable. A better pipeline would make the image look rarer, never less rare.
Searching it is not slow, it is out
At one image a second, exhausting 64×64 takes 10^29,585 years. Every atom in the observable universe drawing one per Planck time since the Big Bang reaches 10^141 images = 10^-29,452 of this format — estimated, assuming about 10^80 atoms in the observable universe; each drawing one image per Planck time (5.39 × 10^-44 s); running since the Big Bang (4.35 × 10^17 s).
The grid is a choice
The totality belongs to the format, not to the world. Move the grid and every number on this page moves with it.
Most tellings of this stop at the size of that set — a very large number, and a suggestion that everything already exists somewhere. The part that survives contact with an instrument is below: the set can never be searched, almost nothing in it has a description shorter than itself, and the totality belongs to the format rather than to the world.
What the numbers are, and are not
Four kinds of number appear above, and they are not interchangeable.
Counted figures are exact arithmetic from the format — how many images it admits, how many digits an address takes, how many variants a perturbation produces. Change the format and they change; nothing else can move them.
Measured figures come from your image this session, through a named instrument. A compressed size is a size under that pipeline, not a property of the image. This matters more than it sounds: a description length is one concrete code length under one serialization, and a different pipeline is entitled to a different answer.
Proved figures follow from a stated theorem. The counting bound is the useful one — fewer than of the strings of length have a description shorter than , because there are not enough short descriptions to go round. It holds in any language, up to an additive constant fixed by the choice of universal machine.
Estimated appears exactly once, for the physical sampling ceiling, and its assumptions are printed beside it. Dispute them freely: the conclusion survives any assumption anyone would defend, which is why showing them costs nothing.
Why a measured length is worth anything at all
A compressor is not an oracle for Kolmogorov complexity. It cannot be — the shortest description of a string is not computable, and no amount of engineering changes that.
What a compressor gives you is an upper bound: if a pipeline writes your image in bits and reads it back exactly, then the shortest description is at most bits, whatever it may actually be. And an upper bound is the direction that happens to be useful here. Every conclusion drawn from it needs only that your image has a description this short, never that it has no shorter one.
So a weak pipeline yields a conservative result. If your image compresses badly under everything on offer above, a better description — one nobody in this page thought of — would make it look rarer still, never less rare. The instrument’s poverty is on the safe side of the claim, which is the only reason it is allowed to carry one.
The map that is not withheld
Two of the operations above deliberately break rules the rest of the page keeps. They are not there for balance. They are there because a rule you are told is a rule you have to take someone’s word for, and a rule you watch fail is one you now know something about.
Project the images onto two axes and you get a picture that looks like a map and carries almost nothing, because in a space of this many dimensions nearly every pair of points sits at nearly the same distance from every other. Your photograph lands among uniform noise not because it resembles noise but because the projection has discarded everything that distinguished them.
Seed the sampler and the draws come from a vanishing subset while looking exactly as they did before. Nothing in the pictures records the change. That is the whole difficulty in miniature: which images a process can reach was never visible in its output, so it was always a claim about machinery — and a claim about machinery is only worth what your ability to inspect it is worth.
Sources
The counting argument and the incomputability of the shortest description are standard; Li and Vitányi’s An Introduction to Kolmogorov Complexity and Its Applications is the reference. Chaitin’s information-theoretic incompleteness result gives the ceiling on what a fixed formal system can prove about any particular string.
The set-of-all-texts idea is Kurd Lasswitz’s Die Universalbibliothek (1901), by way of Borges’ The Library of Babel (1941); Jonathan Basile’s libraryofbabel.info built the browsable version, including for images. The 2025 short film Total Pixel Space is the immediate occasion for this page, and the disagreement with it is the reason the page exists: enumerating the bitmaps a format admits establishes something about bitmaps, not about films, lives, or time.
Compression here uses the browser’s own CompressionStream, specified by the
WHATWG Compression Standard — a deflate-family codec over an ordered byte
stream, which is exactly why its output is treated as one code length rather
than as a measurement of structure.
