Tools and data

Besides the wallpapers, this project produced a few things that may be useful to other people working with fractals.

The atlas for Mandelbrot: the parameter plane in gray, marked with 113 dots, 58 blue for places on the plane and 55 red for the values of c whose Julia sets hold one, each a place good enough for the gallery.

Mandelbrot

The atlas for Multibrot, degree 3: the parameter plane in gray, marked with 85 dots, 49 blue for places on the plane and 36 red for the values of c whose Julia sets hold one, each a place good enough for the gallery.

Multibrot, degree 3

The atlas for Multibrot, degree 4: the parameter plane in gray, marked with 88 dots, 45 blue for places on the plane and 43 red for the values of c whose Julia sets hold one, each a place good enough for the gallery.

Multibrot, degree 4

The atlas for Multibrot, degree 5: the parameter plane in gray, marked with 99 dots, 59 blue for places on the plane and 40 red for the values of c whose Julia sets hold one, each a place good enough for the gallery.

Multibrot, degree 5

The atlas for Multibrot, degree 6: the parameter plane in gray, marked with 40 dots, 21 blue for places on the plane and 19 red for the values of c whose Julia sets hold one, each a place good enough for the gallery.

Multibrot, degree 6

The Phoenix atlas: the classic Phoenix slice in gray, marked with 63 red dots, each a place on the slice good enough for the gallery.

Phoenix, the classic slice

The fractal atlases, one for each plane. Every dot is a place good enough for the gallery.

Every picture in the wallpaper galleries is a place in a fractal and a complete recipe for drawing it there. gallery-locations.jsonl holds all 6,299 of them, one JSON object a line: the fractal family, the center, width, and iteration cap, the rendering mode, the palette and its settings, the collections the picture belongs to, the wallpaper and gallery judges' scores, and a link that opens it in the Mandelnaut Explorer. The link is the whole recipe, so the explorer, or fractal-engine render-link from fractal-wallpapers, will draw any of them again at any size. The file is licensed CC BY 4.0, like the wallpapers. If you want to run the pipeline yourself, Run the pipeline yourself walks through a fresh install and shows what each stage writes.

The explorer's Deep tab also holds a thousand Random dives. They were found by a procedural dive rather than picked or judged, so they are less useful as a list, and it is easy to make more: python -m builder random-dives --until N in the fractals repository lands new ones until there are N. It needs Node and a Rust toolchain as well as Python.

Palettes

Every hand-made palette as a thin strip, grouped by hue in the order of the color wheel and, within each hue, from dark to light.
The 495 palettes I made, sorted by hue.

hand-made-palettes.json holds the 495 palettes I made for this project, as color stops. They are released under CC0, so you can use them for anything, with no credit needed. Each one's name matches its strip on the palette library page, and Make your own palettes describes how they were made. The rest of the library came from other sources and is not included.

Judges

Location judge

Over 226,791 places the walks offered it

A Multibrot d = 5 location, drawn in one neutral palette.

P(=1) 0.98

A Multibrot d = 5 location, drawn in one neutral palette.

P(=2) 0.75

A Julia location, drawn in one neutral palette.

P(=3) 0.92

A Julia d = 5 location, drawn in one neutral palette.

P(=4) 0.98

Wallpaper judge

Over 566,920 candidate pictures

A wallpaper drawn in closest trap angle over smooth, in the Julia d = 5 family.

P(=1) 0.98

A wallpaper drawn in stripe average, in the Mandelbrot family.

P(=2) 0.78

A wallpaper drawn in multiplied trap, in the Julia d = 5 family.

P(=3) 0.96

A wallpaper drawn in smooth, in the Julia d = 4 family.

P(=4) 0.99

Gallery judge

Over the 62,373 pictures in the pool it orders

A wallpaper drawn in stripe average, in the Julia d = 3 family.

P(=1) 0.72

A wallpaper drawn in smooth, in the Julia d = 3 family.

P(=2) 0.48

A wallpaper drawn in stripe average, in the Multibrot d = 5 family.

P(=3) 0.53

A wallpaper drawn in trap spread angle over smooth, in the Julia d = 5 family.

P(=4) 0.64

Palette judge

Its score, over one place drawn in the 32 palettes of one set

The same Mandelbrot location, drawn in the Lemon Ember palette.

score −3.607Lemon Ember

The same Mandelbrot location, drawn in the Chartreuse Marigold palette.

score 0.604Chartreuse Marigold

The same Mandelbrot location, drawn in the Mint Poppy palette.

score 2.640Mint Poppy

The same Mandelbrot location, drawn in the Amber Brick palette.

score 3.835Amber Brick

The same Mandelbrot location, drawn in the Coral Ember palette.

score 5.848Coral Ember

For the location, wallpaper, and gallery judges, a picture each judge thinks most likely to be a 1, 2, 3, or 4, with that probability. The palette judge's row is one place in five palettes, lowest score on the left.

The four neural networks that rated locations and wallpapers, ordered the galleries, and chose palettes are released with the fractal-wallpapers code under MIT, as weights-2026-09-14. Each is a MobileNetV4. Three of them take a picture, stretched to 384×224, and return the probability that it would earn at least a 2, a 3, and a 4 on my 1-to-4 scale. The palette judge works differently: for each place, it scores the place drawn in each of a set of candidate palettes, and its score only means something against the others in that set. They were trained on ordinary double-precision pictures, so read their scores on deep zooms with caution. Training judges describes how they were made.

Hand labels

Places

A Mandelbrot location, drawn in one neutral palette, rated 1.
A Mandelbrot location, drawn in one neutral palette, rated 1.
A Multibrot d = 4 location, drawn in one neutral palette, rated 1.
A Mandelbrot location, drawn in one neutral palette, rated 1.

1

A Phoenix location, drawn in one neutral palette, rated 2.
A Multibrot d = 4 location, drawn in one neutral palette, rated 2.
A Julia d = 3 location, drawn in one neutral palette, rated 2.
A Multibrot d = 3 location, drawn in one neutral palette, rated 2.

2

A Phoenix location, drawn in one neutral palette, rated 3.
A Julia d = 5 location, drawn in one neutral palette, rated 3.
A Mandelbrot location, drawn in one neutral palette, rated 3.
A Multibrot d = 3 location, drawn in one neutral palette, rated 3.

3

A Mandelbrot location, drawn in one neutral palette, rated 4.
A Phoenix location, drawn in one neutral palette, rated 4.
A Multibrot d = 3 location, drawn in one neutral palette, rated 4.
A Julia location, drawn in one neutral palette, rated 4.

4

Wallpapers

A wallpaper drawn in smooth, in the Julia d = 4 family, rated 1.
A wallpaper drawn in smooth, in the Mandelbrot family, rated 1.
A wallpaper drawn in smooth, in the Multibrot d = 3 family, rated 1.
A wallpaper drawn in smooth, in the Julia family, rated 1.

1

A wallpaper drawn in screened trap, in the Julia family, rated 2.
A wallpaper drawn in smooth, in the Mandelbrot family, rated 2.
A wallpaper drawn in triangle-inequality average, in the Multibrot d = 5 family, rated 2.
A wallpaper drawn in smooth, in the Julia family, rated 2.

2

A wallpaper drawn in smooth, in the Mandelbrot family, rated 3.
A wallpaper drawn in screened trap, in the Multibrot d = 5 family, rated 3.
A wallpaper drawn in smooth, in the Julia d = 4 family, rated 3.
A wallpaper drawn in multiplied trap, in the Multibrot d = 4 family, rated 3.

3

A wallpaper drawn in cross trap over smooth, in the Julia family, rated 4.
A wallpaper drawn in smooth, in the Mandelbrot family, rated 4.
A wallpaper drawn in smooth, in the Julia d = 5 family, rated 4.
A wallpaper drawn in smooth, in the Mandelbrot family, rated 4.

4

Gallery pictures

A gallery picture drawn in triangle-inequality average, in the Julia d = 4 family, rated 1.
A gallery picture drawn in triangle-inequality average, in the Phoenix family, rated 1.
A gallery picture drawn in smooth, in the Multibrot d = 3 family, rated 1.
A gallery picture drawn in triangle-inequality average, in the Multibrot d = 3 family, rated 1.

1

A gallery picture drawn in curvature over smooth, in the Phoenix family, rated 2.
A gallery picture drawn in stripe average, in the Mandelbrot family, rated 2.
A gallery picture drawn in smooth, in the Multibrot d = 4 family, rated 2.
A gallery picture drawn in multiplied trap, in the Julia d = 5 family, rated 2.

2

A gallery picture drawn in stripe average, in the Mandelbrot family, rated 3.
A gallery picture drawn in smooth, in the Multibrot d = 5 family, rated 3.
A gallery picture drawn in stripe average, in the Multibrot d = 4 family, rated 3.
A gallery picture drawn in smooth, in the Mandelbrot family, rated 3.

3

A gallery picture drawn in cross trap over smooth, in the Mandelbrot family, rated 4.
A gallery picture drawn in triangle-inequality average, in the Julia d = 4 family, rated 4.
A gallery picture drawn in curvature over smooth, in the Multibrot d = 3 family, rated 4.
A gallery picture drawn in triangle-inequality average, in the Multibrot d = 4 family, rated 4.

4

Four random pictures I rated at each score, 1 on the left to 4 on the right: places, wallpapers, and gallery pictures, top to bottom.

The ratings I gave while training the judges are in the fractal-wallpapers repository under data: locations in data/labels, wallpapers in data/smooth_render and data/strange_render, and gallery grades in data/gallery_grade. A wallpaper or gallery rating is stored with the complete recipe of the picture it rates, and a location rating with the place and the settings it was drawn at. Aesthetic ratings of fractals are rare, so they may be useful on their own.