How this got here
It began with a video game from 2008 and a set of names somebody deleted.
Mercenaries 2 keeps 9,539 bone hashes and no names. The hash is weak enough to guess against, so finding a string that produces a given one is easy, and I wrote a tool that does exactly that. Feed the engine a colliding string and it loads the bone quite happily, because the engine only ever knew the number.
But a working handle is not the name. It is a nonsense word that happens to collide, and what I wanted was the word a developer typed in 2007. Those two are indistinguishable by arithmetic. The thing that separated them was not more computation; it was information from outside the hash entirely. Every bone has a position, and a bone at the front left of a vehicle, low down, near the ground, is a wheel.
Asking that question meant plotting nine and a half thousand points in three dimensions and turning them around to see whether anything clustered. That program is where the camera came from, and it explains something that would otherwise look strange about it: it does not draw surfaces. It has no polygons and no shading model. It accumulates points, one at a time, because it grew out of something written to look at a cloud of positions and work out whether they meant anything.
Something can work and not be true
A glow added because it looks nice is a colliding string. It works and it means nothing, and worse, it is unfalsifiable. If the corners are soft because I decided they should be, nothing about the picture can be wrong, and a picture that cannot be wrong cannot be right either.
So the instrument was made real in every respect that could be made real, and then allowed to do whatever that turns out to make it do. The rules are not mine: diffraction at a circular aperture has one answer, a Topogon has the field curvature it has because Robert Richter chose those radii in 1933 solving for aerial survey, and the glass catalogue is published by the people who melt the glass. Each of those is a place this work touches something outside itself and can be found wanting.
Who is doing this
I am a carpenter. I am not a mathematician and not a programmer by trade, and I did not choose the Hopf fibration because I understand fibre bundles. I chose it because it is a few lines of arithmetic that produce something no drawing can honestly show, and I wanted to look at it.
That turns out to disqualify nothing, and I think the trade is why I was comfortable with it. A carpenter works to a measurement. You do not need a theory of timber to build a straight door; you need to know what the material does, to check the thing you made against a number rather than against your own opinion of it, and to be honest about the tolerance you actually held. That is the entire method here, applied to a different material.
The practice has a name
Photography whose subjects are mathematical objects, found rather than made, is platonography, and the instrument that practices it at large format is the Eidograph. Its biggest photographs are too large for one person to back, so they are computed as public works: anyone with a graphics card can render a piece, donors verify one another, and the picture paints itself onto a public page as it arrives. The works live at platonography.com.