Finding good wallpapers — Making Fractal Wallpapers

Finding good locations ends with a stock of rated frames, none of them yet drawn as anything a person would want on a screen. But a location isn't a wallpaper yet. The same place can be beautiful in one rendering mode and dull in another, striking in one palette and muddy in the next. Turning a stock of places into a stock of pictures is its own problem, and it is where most of the project's rendering time goes. When I mine, I don't limit myself to what the search admitted: I can try any location the location judge isn't confident is junk, because I treat that judge as a hint about where to look, not a verdict on the picture.

One location the search admitted, drawn in one neutral palette. — The three parts, and what each hands to the next. The top band is sixteen places the search admitted, all drawn in one neutral map because nothing about their color is settled yet. The middle band takes the marked one: two of its best results in different rendering modes, and two in different colors. The bottom band is eight seats from a curated gallery, chosen out of the pool.

How one picture is made

The unit of work is one small picture, and making one is always the same four steps.

The location's smooth field is computed once, at a small size: 640 by 360, the geometry the judges were trained at. The thirty-two-palette neighborhood from color palettes is built over that field and the palette judge picks one of them. The rendering mode being tried then draws the picture through the chosen palette, as rendering modes described, at that size with two-by-two supersampling, and the wallpaper judge scores it. Only the plain field modes read the same field the palette was chosen on, so the palette is usually picked on one picture and spent on another.

What that produces is a candidate: one location, one mode with its settings, one palette, the judge's scores, and the small picture itself. Everything else on this page is about which candidates to make.

One cost saving shapes all of this. For the modes that read a single scalar field, the field can be computed once and then colored many times over, so a second look at the same place in the same mode costs a coloring rather than a render, and even autolevel's second pass is another coloring. The composite modes, the direct traps, and the mode that shifts where each sample reads in the map build their pictures differently and have to be drawn in full each time.

One location through one attempt: its smooth field as plain lightness beside the same location in the rendering mode the attempt drew, then a block of thirty-two colorings of that field with the chosen one outlined, and last the small render that is judged. — One location through one attempt. The palette judge compares thirty-two colorings of the location's smooth field and the outlined one is its pick; the mode beside it is what the picture will be drawn in. The last panel is the picture the wallpaper judge scores.

The pool

Every mine, one session of this drawing and judging, empties what it made into a single pool, and a gallery is chosen from the pool as a whole rather than from whatever the last session happened to produce. The pool does not simply grow. Each time a mine merges into it, only the best few candidates at each place and mode survive and the rest are deleted, so what builds up over time is coverage: more places, tried in more ways, rather than a larger and larger heap.

I keep the pool separate from the mining that fills it. That way a place found once is found for good, and a mine never has to justify itself by what it ships. It is adding to a store rather than putting a collection together, which leaves it free to spend a whole session on a single question.

Breadth and depth

Mining has two uses for a budget and they compete. Breadth opens places the pool holds nothing for, a few attempts each, modes cycled so no one mode takes the whole visit. It is deliberately shallow: a few looks are enough to learn whether a place can give anything, and a palette sweep everywhere would buy that same answer at many times the price. Depth goes the other way and holds one location and one mode while it tries many more palettes there. It is worth most where the field is already computed, or where the candidate standing at a place sits just under the bar and another palette might carry it over.

One attempt of the mine at this location, drawn in curvature over smooth, with its palette's gradient under it. — One visit to one location, in five of the seven modes it drew. A mine that reaches a place cycles through modes and tries a few palettes in each; none of these five has a scalar field to reuse, so every picture here was drawn in full, and the visit's forty-four attempts took 42 seconds in all. Under each picture is the wallpaper judge's score and the fitted rank the pool orders on, and the outlined ones are the ones the pool still holds.

Where the budget goes

Mining time is finite, and how I spend it decides what the collection can contain. I mine until the pool holds what a gallery needs, and let the gallery tell me when it doesn't. A general mine draws its modes uniformly over the whole roster, and most of its time goes to the modes that must be drawn in full, because they are most of the roster and each costs several times what a recoloring does. They are also the ones a gallery is most often short of. When I choose a gallery and it comes up short, the shortfall names the modes, colors, and families it lacked (gallery curation), and I mine longer rather than mining differently.

Keeping only what earns its place

A mine that visits a location many times produces many pictures of it, and keeping them all would fill a disk with variations nobody will ever choose between. So the pool keeps the best five candidates of each location and mode, ranked among themselves. A mode drawn with its settings changed keeps its own five rather than competing with the mode's default.

How candidates are ranked

To rank candidates within a location I need one number, and no single judge's output gives me that. The wallpaper judge's score at its top threshold comes closest, but as training judges described, it doesn't have much resolution left among the good ones.

So the prune ranks on a fitted combination: the location judge's own opinion of the place, the wallpaper judge at both of its thresholds, and a measure of how much of the frame is dead flat space. I use it to order candidates, not as a bar. When I fitted it, it beat the wallpaper judge alone, but that advantage didn't survive the label corpus tripling: refitted today it adds nothing over the top-threshold score, because the judge itself got better. It stays as the prune's order, and newer ranking ideas, the gallery judge among them, are tried first in gallery selection, which can be taken again, rather than in a prune that deletes.

The pictures that make it through all of this are the pool that gallery curation chooses from.