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I'm looking for more variants on the "Julibrot" projections- real plane, imaginary plane etc. particularly for Ultrafractal. As far as i know there's only one in the UF formula database, and it doesn't allow you to select other exponents than 2.

can you name the formula path ?  O0

i can adjust it for you if you like ...

There's a really old formula called "4D Transform" in mmf.ufm.
It allows you to rotate the 2d image as a slice from the 4 dimensions made from zstart and the Julia seed, with 12 rotation angles and positioning of the 4D centrre.

Apologies - I failed to notice, it also lacks the "power" option - I can add it if you like ?
However it does allow some formulas other than just z^2+c.

I always found these alternate projections very "underrated" among fractal artists, and i find it somewhat strange that they're not covered more, and seemingly almost never used by artists.

They would be great for zooms and animations, since they vary a lot from place to place and do not simply repeat like Julia sets. And i've yet to even see what they look like for the more unusual formulas, like Magnet, Nova, Newton or Herman Rings.

I think an UF formula should concentrate on the six "basic" projections though, rather than arbitrary angles - formulas with too many parameters always scare me.

(Also they tend to be excrutiatingly slow to render, though this might just be to poor programming, or optimization.)

Another possibility i don't think have been tried is varying the power along one of the axis, rather than Z or C.

If you look at the switch formulas in mmfs.ufm or some of the "Switch" class formulas in mmf.ulb (advanced parameters) you'll see I've allowed the option of rendering such that the complex viewing plane for the Mandelbrot version gives variables in the formula other than "c" - such as the power.

For example in mmfs.ufm:Switch Standard from the default change the "Current mode" parameter to "Mp(Zstart)" (stands for Mandelbrot power Switched value replaces zstart) and change the "Switch using" parameter to "J(Power)".

Or load mmf5.ufm:Generic Switch Formula and in the Switch Standard formula enable the "Enable Advanced Settings" parameter and the viewplane is changed in the Mandelbrot to be the power rather than "c" - you can try different values of "c" on the Mandelbrot by exploring the "Seed" parameter. Obviously switching to the Julia gives you a Julia with the power taken from the switch location and "c" taken from the seed.

I just uploaded a new version of mmf.ufm to the UF formula database with a change to the 4D Transform formula so it has a power parameter for the Standard formula option.
As to the speed, it seems pretty quick to me :)
Having said that it could be a lot faster because when it was written (for UF 2) there was no global section in formulas so the 4D rotation set up had to be done in the init section i.e. per-pixel rather than per-screen.