Pauldelbrot's Ultra Fractal colouring formula

[Pharmagician]

I've been watching and admiring Pauldelbrot's various series (Mandelbrot Safari, Twistor World, Seahorse Odyssey) for a long time now and have been knocked out by the colouring of these images.  Pauldelbrot then very generously wrote and shared here a colouring formula for Ultra Fractal that does things in a similar way to his own personal software.  I've been playing with his formula a lot and this is one of the results, and here's a link to it on dA for a fullsize view: http://pharmagician.deviantart.com/#/d4w068y

Thanks again Pauldelbrot!

[cKleinhuis]

thank you for notifying, love the green dot

[Pauldelbrot]

Excellent. Glad someone else is getting nice results with this. It seems in particular you've found how to use varying saturation to nice effect.

[cKleinhuis]

you know, pauldel i will have to do an own tvshow of this, can you explain with 3 sentences what your coloring method makes special ?

[Pauldelbrot]

It's fractal.

Well, almost. It has detail at several length scales, waves of changing colors or luminances with different periods. So it can make features have contrast at different "iteration scales".

[end of the quick synopsis]

In Pharmagician's image, you'll notice how seahorses and their spirals contrast with their backgrounds, and the seahorses' eyes are different brightness and hue from their fringes, and the "rune" like features contrast in color from their surroundings, and a whole new color (green) comes in in the very middle.

For UF users, importantly, this can all be done with a single layer, saving a lot of time, particularly with deepzooms.

It also can "discover" interesting new color schemes for you, in a way, because you don't micromanage it and the machine can surprise you. I got the very pleasing browns/yellows/muted reds in the second-to-last segment of "Change" partly by happy accident.

A downside of the UF version is that changing anything requires recalculating the whole image, and generating a color cycling animation in particular would therefore require calculating every frame. If I'd had to do that, I couldn't have possibly rendered "Change" by the deadline and had time for everything else as well -- in fact I needed only a few hours to render "Change", of which 45 minutes was spent computing the lightning image which is arbitrary precision by a small bit and heavily antialiased. There are 720 frames in the segment with the lightning image; if each one had had to be calculated from scratch, taking 45 minutes per frame, it would have taken 540 hours to render that segment, or 22 and a half days -- that is, over 2/3 of the submission period would have been spent on rendering just 30 seconds of one video!

[Dinkydau]

Do you think it would be possible to achieve such things in fractal extreme? I've been experimenting with colors there but this requires new code.

[Pauldelbrot]

It doesn't seem likely. AFAIK there's no way to color in FX other than with the built-in gradient editor and a few options. You can't even stretch a logmap over the observed span of iteration counts in the image, I don't think, and there's certainly no hook for user-defined coloring rules.

In theory, something like this (plus smoothed iterations) wouldn't be difficult for the author to add. It only needs the final z and iteration count, rather than per-iteration extra processing in particular (unlike, say, DE, or Dwellgrad, or exponential smoothing, or orbit traps).

Problem is, FX hasn't been updated in years and it's proprietary, so nobody else can take over and make new versions and improvements.

[Pauldelbrot]

There's a thread in the UF forum here with an attachment with the multiwave .ucl for anyone who's interested.