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I took a slice of a degree 6, and found this ..
Seems like all the familiar fractal shapes are to be found on the inside.
(image : Ultrafractal)

Yes indeed :)
It looks even better with some angle in the view:
(http://www.fractalforums.com/gallery/1/492_20_11_09_8_03_11.jpg)

Or even better with nice perspective like in this image from Buddhi:
(http://www.fractalforums.com/gallery/1/640_01_12_09_10_02_34.jpg)

pretty neat :)

any cutplane-rotation animation yet?

Can't beat Bib's pictures!
Bib, what power is this and what cut did you take?

thanks :)
you'll guess the power (2) and the cut plane from this image :
(http://www.fractalforums.com/gallery/1/492_15_11_09_8_03_50.jpg)
http://www.fractalforums.com/gallery/1/492_15_11_09_8_03_50.jpg

Actually I just found how to do like Buddhi's perspective using David's formula in Ultrafractal, but it's not easy to find the right parameters (Camera distance and Image Plane distance)

If you bear in mind that the "Camera distance" is simply the distance of the image plane from the target and will not change the perspective when modified (only changing the camera location) and the "Image Plane distance" is the distance of the image plane from the viewpoint and will change the perspective when modified then you should be OK !
Note that one thing you can try for easier positioning is set the "Camera distance" to a very small value (e.g. 0.000001) and then the "target" is effectively the location of the image plane, in other words the target location becomes the camera position. Don't use zero for the "Camera distance" though because that'll screw up the camera rotation.
If you want things to look like small objects then use a large image plane distance, but if you want to make things look huge then reduce the image plane distance (e.g. to 0.1 or even less), reduce the distance of the camera from the desired view area and increase the magnificatiion.


BTW I am working on an updated formula (probably to be released as a separate formula rather than an update) that will render everything based on the Mandelbulb method considerably faster.

Are these mandelbrot-like slices taken through a random plane? because if they're taken through i=0 or r=0 then it is clear that they will have mandelbrot-like detail because the equations are just mandelbrot-like equations.
If they are really from a random plane then that is more significant, more surprising and more interesting.

no miracle unfortunately!

EDIT : however if you rotate the cut plane 90° around the main axis, you get new kinds of shapes like:
(http://www.fractalforums.com/gallery/1/492_16_11_09_11_33_06.jpg)
http://www.fractalforums.com/gallery/1/492_16_11_09_11_33_06.jpg
(http://www.fractalforums.com/gallery/1/492_16_11_09_11_21_29.jpg)
http://www.fractalforums.com/gallery/1/492_16_11_09_11_21_29.jpg

@David, I'm trying hard but it's still unclear to me. For example if I take the first image I posted above and try to apply more perspective, the location is completely screwed up. Starting from the general view I posted just above, what operating mode would you suggest to do a similar image as Buddhi's one (the 2nd one) ?

Ah, I think I understand your problem - I assume you positioned things using UF's standard zooming ? If doing that you change UF's centre from (0,0) then it causes problems setting positions up using the formula parameters. Ideally you should get the image set up as best you can with UF's location fixed and only change the magnification value and the formula parameters to set the position and distance etc. If you change the UF location so it's not centred then any changes you make to the formula parameters will always completely change the view.
So if you want to start from the image you posted then the first thing to do is reset UF's in-built center to (0,0) then use the formula target/distance/rotation to get a similar view to what you started with. As I said above a trick you can use here is set the "Camera distance" to a very small value, that way the target location is effectively the camera location. Obviously you can set a camera location then use "explore" on the camera rotation to point it in the correct direction.
Note that a trick to find the x,y,z value for a given location is make sure UF centre is zero with magnification 1 and the camera target is (0,0,0) with a normal camera distance, say 4 or more, then set the formula to "parallel" instead of "perspective" and view at (0,0) camera rotation and UF's x,y coords are the 3D x,y coords, then rotate the camera 90 degrees (direction not elevation) and you then have UF's 2D coords as the 3D z,y coords (or -z,y).
It's best to completely use the formula parameters for setting up positions, just changing the UF magnification until you're very close to what you want and then finally use UF's zoombox to relocate/frame exactly as you want things at the end.

You're right and I suspected exactly what you explained about UF's location that should be set to 0.

But there is a kind of bug in the "explore" window when playing with camera position/rotation: it does not take into account all parameters (I don't know which ones exactly) so the preview image is not the result you get. It makes the process trial and error oriented and quite tedious.

You guys never cease to amaze me. Especially considering that your renders probably take minutes to hours and take even longer to prepare.

If you don't count the time taken writing and optimising the actual formula used then this one http://makinmagic.deviantart.com/art/Summer-on-the-Tundra-145532566 (http://makinmagic.deviantart.com/art/Summer-on-the-Tundra-145532566) took only about 5 or 10 minutes to prepare, though admittedly the render took an hour and a half @3840*2880 - but that's only on a core2duo, maybe 4 to 5 minutes on a dual quadcore :)
You must remember that in normal UF formulas you can work on an image without having to wait for each change to finish rendering, you get to see lower resolution previews when using "multi-pass" mode.

That's strange, I've never noticed such a problem...will investigate.

Can't find a problem, but, you do know that the preview only shows the selected layer and not all layers ?

Yes I know. I will try to make some screenshots and post an upr for the example.

The design time is a hobby. But the calculation time is a pain!

I have one animation in the render queue (a "remix" of my previous Mandelbulb crater tranformation, with a better codec) that starts with a 5 sec dezoom from this kind of spiral. Hopefully it will be finished in a week or 2.

@David,

Is it possible to achieve parallax zooming (and avoid the "zoom in a very large still picture" effect) by carefully choosing parameters ?

Yes, use a small Image plane distance and suitable (fixed) high UF magnification and do all the rest using the target/distance/rotation parameters - I'd suggest setting the "camera distance" also very small and then the "target" location is effectively the camera location then you can move the camera to exactly where you want it by simply changing the target location.
This way to zoom-in just move the camera position closer to the object rather than using UF's location/zoom.
You can also get interesting effects by animating the image plane distance and the magnification together, done correctly the image in the view will remain constant but simply change perspective.

Aaaaargh!  :( :( ??? :hmh: :tongue1: :'( :'( :D
Try for example to "explore" any Viewing control parameter in this upr and tell me if what you see in the Exploring window is consistent.

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Aha, it seems you have discovered a bug in Ultra Fractal.
What's actually happening is somehow UF is showing a preview of a modification of the wrong frame of the animation.
I will forward to Frederik :)
There is a somewhat clumsy workaround - duplicate the fractal, delete the animation from the duplicate (don't change frame but bring up the "timeline" right-click on the top bar and select "delete selected"), now the explore preview will work on the duplicate. Finally copy the rotation parameter from the duplicate to the appropriate frame in the original (obviously in "Animate" mode).

I had just noticed that in animation with only 2 keys, while exploring the last frame, it shows the 1st one in fact. The workaround seems logical. Anyway, I've been trying to do some parallax zoom, but I'm not satisfied at all. For example I find the camera distance difficult to manipulate, not linear, and I sometimes it suddenly clips parts or the whole image with a very minor change (but that's typically a fractal behavior :))

This test video is funny:
http://www.youtube.com/watch?v=T28_tcbX1Mk

You can avoid the clipping to some extent by setting the front clipping plane so it's closer to the viewpoint than the image plane - to do so use a negative value for the front clipping plane position parameter (use a slightly smaller value than the image plane distance e.g. if the image plane distance is 0.5 then use say -0.45 for the front clipping plane).
The other thing to avoid the problem is to increase the magnification.