TL;DR: a brush engine that produces natural-looking strokes by incorporating the stroke within itself.

Drawing programs makes the brush strokes appear natural by using scanned images as brush tips. This works rather well, but has the limitation that the scanned image in itself is static. The splashes of ink may have reacted naturally to your hand movement when it hit the paper, but once it scanned, it becomes static: It is merely an image of something which was once reacting naturally. Regardless whether you make a stroke long or short, soft or hard or whatever, the brush tip itself is still static.

Now, I mean no disrespect towards bitmap brush tips. They're great. I have spend a lot of time creating them. But wouldn't it be interesting with brush tips that weren't static, brush tips that reacted naturally to the stroke itself?

I propose an entirely new brush engine, based not on a static bitmap, but on the natural principle of self-similarity. And no – I'm not some pothead suggesting ideas that sounds grand in theory but is impossible to implement. This can be done relatively easy. ("relatively")

Alright then. Self-similar visuals have a specific style, marked not by any specific patterns or shapes, but by the recursive repeatition of themselves.

Fractals are examples of 'perfect' self-similarity: The repeats are 100 % exact, and thus, we can zoom in forever.

Natural self-similarity, such as trees, mountains and ferns, are not perfect. If you zoom in on a mountain range, it looks kinda similar to the larger view, but it is not the same and thus, we can't zoom in forever.

And what's good enough for mother nature to do her thing is also good enough to construct our brush engine. We do not need perfection. As long as we somehow implement the basic principle of self-similarity, it is of little importance how we archive that goal. We don't need to dig into fractal math or things like that.

What is needed is some clever hack. My suggestion is this simple idea: The brush tip used in the stroke is the stroke itself!

I have tried to visualize how this may look:
https://s10.postimg.org/kxrwxulop/fractal_brush_engine.jpg

I think such an engine could be used to create a great variety of brushes, when combined with various seed brush tips, spacing, rotation behavior, and if these settings could be adjusted independently in the seed and 1st and 2nd generation.

… Thanks for reading this far! As a reward, here's two vids on fractals:

Fractals - Hunting The Hidden Dimension (HD)
https://www.youtube.com/watch?v=s65DSz78jW4

Old VHS rip: Arthur C Clarke - Fractals - The Colors Of Infinity (1995)
https://www.youtube.com/watch?v=Lk6QU94xAb8

Okaaayy then,

I don't quite see the practical use of such a brush engine.
Sure you could make some wild fractal brushes, but is that really what a lot of painters need? I doubt it.

If we implement new brush engines they really have to be useful to many artists. I think the majority
of artists don't use any other brush engine than just the pixel engine. They barely use different brushes.

I would also dispute the simplicity of implementing this idea, but okay.

I think this idea belongs much better to a program like Alchemy where people experiment with brush shapes.

Interesting

Hi Nim, thank for your feedback! You asked what the practical use would be for a fractal brush. Okay ... I think digital artists have left the classic airbrush brush behind because its expression is weak and boring. What make the painting media stand out is the medias own expression: There's a lot of difference between the expression delivered by water color, wood cuts, pencil drawings, oil paint or pastel. The best artist avoids letting the painting be 'overworked', and instead lets the medias own expression speak out. Generally, the artist allows himself to 'overwork' the paintings focal points, like eyes or boobs, while letting the rest be a bit more sketchy. Take a look at this image by Frank Frazetta. Check the rawness of that background! More extreme: Whistlers Nocturn in Black and Gold.

My point is that the expression of the medium is not just a gimmick or a fault. It is its foundation. In digital painting, that foundation is artificially designed. If we can articially emulate the pencil medium or the paint medium, then it may also be possible to articially design naturally behaving medias that do not exist in the physical world. The practical use of an fractal brush would be a brush with an expression that appears natural, since fractal-like shapes are a natural occurence. I hope for an expression akin to that of Encaustic painting, but far less cucumbersome than that medium!

Here's another way we could create a fractal brush: Each new brush stroke replicate the collected brush strokes. So when you make three strokes, each stroke display the three strokes. Example here!