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Previous tries were so ugly, that I decided to start new thread in place of this http://www.fractalforums.com/new-theories-and-research/end-of-greatness/ (http://www.fractalforums.com/new-theories-and-research/end-of-greatness/)

With third try it looks that I succeeded with gravitational waves swirls. It don't looks like large scale structures of universe (in 2D it looks so), but discontiniuaty along y=0 or x=0  is eliminated and now it is smooth.

radius = sqrt( sqr(zx)+sqr(zy)+sqr(zz) );

angx=atan2(radius+1i*zx);
angy=atan2(zx+1i*zy);
angz=atan2(radius+1i*zz);

zx= cos(frequency*radius+ spin*angx) *radius*scale+Cx;
zy= sin(frequency*radius+ spin*angy) *radius*scale+Cy;
zz= sin(frequency*radius+ spin*angz) *radius*scale+Cz;

Maxiter =4, bailout =5, scale =1.5. frequency, spin and scale are paeameters.

(http://www.ljplus.ru/img4/a/s/asdam/Grav_swirl_1.jpg)

(http://www.ljplus.ru/img4/a/s/asdam/Grav_swirl_2.jpg)

(http://www.ljplus.ru/img4/a/s/asdam/Grav_swirl_3.jpg)

(http://www.ljplus.ru/img4/a/s/asdam/Grav_swirl_5.jpg)


Exponent smoothing coloured 2D with secondary swirls looks like NGC 3810. Of corse galaxies tend to be thin.
(http://upload.wikimedia.org/wikipedia/commons/thumb/c/c2/NGC_3810_%28captured_by_the_Hubble_Space_Telescope%29.jpg/220px-NGC_3810_%28captured_by_the_Hubble_Space_Telescope%29.jpg)

well, those do look quite wild. :)

Have you seen my notes on the other thread?

Yup. Throught if considering it's in 3D, formulas seems far above my math abilities;)

It does not look much like a gravity swirl ^-^

it mostly just looks swirly.
You gotta keep in mind that this mandelbrot-esque iterative process isn't in any way related to what's actually going on in physics, so the results are arbitary.
Still, it could become something nice with some more tweaking :)

Well, with introduction of 3rd dimension swirl turns into something chaotic :hurt: In 2D it's still good old e^i(xy) spiral.

In 2D I got something that resembles, what would be expected from gravitation. IMHO, it could something to do with, throught of corse it is very far away http://en.wikipedia.org/wiki/Density_wave_theory (http://en.wikipedia.org/wiki/Density_wave_theory)

Don't worry, it's all about you consider a success ;D

Our goverment have very interesting wievs of what constitute success  :hurt: :banginghead: :vomit: :sick: , but l think this is not so :hurt:
 
This should be analog of 2D swirl transform. I had a bitt of free time spend on searching for parameters and wievs, so I made slices from z= 0 to 0.75-1. In the XY cutout it have the same swirls as in 2D.


bailout=7 frequency=6 spin=3 scale=1.5 maxiter=4
(http://www.ljplus.ru/img4/a/s/asdam/Grav_Swirl_alpha_3D.jpg)



bailout=6 frequency=6 spin=8 scale=1.75 maxiter=3
(http://www.ljplus.ru/img4/a/s/asdam/Grav_Swirl_beta_3D.jpg)



The same in ZX. Still swirls, but z=0 have some feature which don't appears in xy.
(http://www.ljplus.ru/img4/a/s/asdam/Grav_Swirl_beta_ZX.jpg)



And in ZY. Almoust no swirls. And axis of rotation or some feature of how trig is executed or something on z=0???
(http://www.ljplus.ru/img4/a/s/asdam/Grav_Swirl_beta_ZY.jpg)

those are quite beautiful and remind me a bit of agate stone slices.
(http://www.juniorgeo.co.uk/images/Smagateslice.jpg)

Thanks. Stone slices looks tasty, a like some exotic fruits.
But that ugly line looks like some kind of rotation / symmetry axis, sugesting that it woun't be easy to get rid of it.

I wouldn't sink my theeth into them though. They're kinda hard and taste a bit like earth but dryer.

No axis or other unnecesary features here. Just rotated and cutted fractal of above.

(http://www.ljplus.ru/img4/a/s/asdam/Grav_Swirl_alpha_Choped.jpg)

Interesting, if there are mandelbox with rotation aka rotbox, could there be swirlbox?

sure there can, i am talking my mouth all the time to include basic transforms in the hybrid process, beginning with
the most basic transforms "add", "mul" but basically ALL flame transformations should be made available for the hybridisation process....

this clearly shows some neat, swirly, surprisingly irregular patterns.
What iteration counts are you using?

I used just 3 - 5 iterations, no more.
IMHO flame transforms should be adapted to 3D first. This was an adaptions, cos there were no formula for z axis.


From the cutouts above I tweaked Dahlia. Without cutouts it is more like onion:
(http://nocache-nocookies.digitalgott.com/gallery/13/5956_11_01_13_11_03_58.jpeg)

ok, but most transforms are easily extendible to 3d at least most of them ;)

cKleinhuis: There is no obvious way how to turn a 2D spiral into a 3D spiral. You can do some things but none of them could really be considered "natural" extensions.

One idea would be to simply add a linear component to the z-axis, making it a tapered helix or a spiral on a cone.
Using the logarithmic version instead would make it a logarithmic helix, looking like a path a particle near a black hole might be imagined to take. (The actual paths such particles take would be much more complex, I guess)
Other ideas:
http://en.wikipedia.org/wiki/Spiral#Three-dimensional_spirals

some transforms are harder than others, when browsing through the apophysis code, most functions are easily extensible to 3d ;)
lol, might result in completely different transforms, but would be worthwile to transform most of them ... ;)

I'm not shure how does Apophysis transforms works. Maybe UF pixel mapping functions would be more easy, but Apophysis images are more favored in deviantart, so there are something.

(http://nocache-nocookies.digitalgott.com/gallery/13/5956_14_01_13_3_34_10.jpeg)


I also made box fractal based on swirl transform. Modified abox fold based on abs function, then 3D Swirl, then Scale and +c. Still must be tweaked. So far it looks like int folding, but there are hidding spirals. 
(http://www.ljplus.ru/img4/a/s/asdam/Swirlbrot_test.jpg)

I think, 3D fractals and transformations could be based on vector math.
I was thinking, what would be, if Z is 3 variable vector, then to this vector is added perpendicular vector with lenght 1, then another perpendicular vector with lenght 1, and then C, or something like that, to create square or cubic orbits, which wount escape for some few 3-10 itertions.

nice :)