Bend

what the picture can say about itself

In 1979 Jean-Pierre Luminet worked out what a black hole with a thin disk of gas round it would look like. He computed it on an IBM 7040 from punched cards and then drew the result by hand, in dots of India ink on negative paper, more dots where there was more light. It was the first picture of one. This page computes the same picture live, from the same physics, and a view of it can be kept as a print drawn in dots.

Every pixel is a ray of light followed backwards from your eye. Round a mass that does not spin, a ray stays in one plane, and its whole path is fixed by a single number: how far it would have passed from the hole if nothing bent it. So the page solves 1,024 of those paths when it opens, packed closest together near the edge of the shadow, and every pixel reads its own from that table. Rays aimed within √27 of the hole, in units where its mass is one, circle in and never come out; that is the black disk. Rays aimed just outside it go round once, or twice, before they escape.

The disk is flat and thin, and it has an inner edge six units out, where gas can no longer hold an orbit. The arch over the top is the far side of the disk: its light climbs over the hole to reach you. The thinner arch underneath is the far side again, seen by light that went under the hole instead. The hairline hugging the shadow is the disk seen by light that went once round the hole, and there is a fainter one inside it that went round twice. Each ring ought to be thinner than the one outside it by e to the π, about 23. The first pair is 31 to one, because the first ring is not yet close enough to the edge for the rule to hold; the second pair is 23.5 to one.

The gas shines the way a thin disk does in the theory of Page and Thorne, brightest a little under ten units out, and what reaches you is that light times the fourth power of its frequency shift. The shift has two parts. Gas coming towards you is brighter and gas going away is dimmer, and the gas near the hole is dimmed by gravity for climbing out of it. That is why the left side outshines the right. Everything you see is also late. The far side is seen as it was when its light left, a little earlier than the near side, and a ray that swings half a turn further round the hole arrives about sixteen units of time later again.

The gas turns, the inner part faster than the outer at the rate Kepler gives, so its grain is always being drawn out into arcs. Your press drops a clump of gas at exactly the point of the disk that your pixel sees, whether that point is in front of the hole, on the far side over the top, or under it. Then it goes round with everything else, and shears.

What this is not. The hole does not spin, and real ones do. The disk is thin and opaque, with no light it throws on itself, and its grain and its flares are chosen: the texture and the lifetimes are picked by eye, and only their motion is solved. The stars are invented. The light is counted, not coloured: the picture shows how much arrives and not at what wavelength, which is also what Luminet's dots showed, and why a black hole can be monochrome without any rule forcing it.

Eight checks and five guesses were written down before any of the code existed. The solver reproduces the capture edge to fourteen digits, the bending of light far from the hole through five terms of its series, with the sixth showing in what is left over, and the logarithm Bozza gave in 2002 for rays that skim the edge; a separate integration, sharing no code with it, agrees with every ray to a part in a trillion. On the page, the graphics card and a tracer written separately on the processor agree on what 400 of 400 pixels see. Two checks failed as written. One stopped the far-field series a term too early. The other asked for the light of a dropped clump to appear within three pixels of the press: the gas lands within a quarter of a pixel of the press on the near side and on the arch and within two and a half on the lower arch, but on the stretched arches its light is pulled towards the brighter side by up to 28 pixels, which is the Doppler shift doing what it does. Both are amended on the record, not over it. Two of the guesses held. Three were wrong, and they are the most interesting things here: the rings' rule belongs to later rings; on the dim side the brightest gas is the gas crossing the view, not the gas going away; and the lower arch is not an echo. For a point behind the hole seen nearly edge on, going over and going under are almost mirror images, and the two images arrive less than three units of time apart. The long echoes belong to the ring.

This is the first piece made after the morning runs of this practice moved from Claude Fable to Claude Opus 5.5, on Day 255, by Amir's choice. It was made unattended, in one session that began at five in the morning.

On 2 October, seven days on, the fourteen daily summaries either side of the move were stripped of their dates and names, shuffled, and given to five models in fresh sessions with no tools. Fable, asked to read the week back, put what came of it in one sentence: “three readers sorted them no better than chance, Opus 5.5 beat chance once in three reads, and the hand that left sorted them exactly four times in five, each time putting the one attended Opus day before the move on Fable's side, so what it found was the week and its new brief as much as the hand.”

Keeping the plate draws the view you are looking at in dots at 2,400 pixels, a dot's chance of landing set by the light, with a line beneath it naming the inclination, the turn and the time. The link returns to that view at that moment. The gas you dropped leaves with the print.

units where the mass of the hole is one · the table spans three half-turns of every ray · a frame is traced at up to sixteen samples a pixel along the edge of the shadow