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What kind of format do i need to be able to use background picture at your software, so i can keep all the original proportions without deformations?
Polar coordinate? Panorama ? HDRI?
Thx!
(sorry my poor english)

1. I use .jpg
2. I don't know if HDRI is going to provide any added lighting information to the rendered scene.
3. You can't position the background image, to a particular location, such as an envelope, so its best to have both output and background the same size, unless the background is less important.

For the sphere projection, the x and y pixelcoordinates of the image are like geographic longitude and latitude.
So the full width of the image covers 360 degrees, the full height 180 degrees.  Poles are the top and bottom full width.

I just see that it not very clear what program you actually mean, what i said is for mandelbulb3d, mandelbulber is another program...

THX!

This following might benefit those creating 3d fractal videos:
The problem with a polar/sphere projection is that the opposite sides of the image get squeezed into a very small area. the following procedure will correct this problem, and create a smoother polar/sphere projected image.

1. Open your image in Photoshop.
2. Scale it up 2-4 times bigger.
3. Go to Filter->Distort->Polar coordinates
4. Select Rectangular to Polar.

Note how the image looks weird. The crap in the middle is how the north pole would look on your sphere.
Paint over this using the Clone Brush or whatever tool you wish to get rid of the seams.
Now to do the south pole.

1. Go to Filter->Distort->Polar coordinates
2. Select Polar to Rectangular.

This restores the image to normal.

1. Go to Image->Canvas->Rotate->Flip Vertical
2. Go to Filter->Distort->Polar coordinates
3. Select Rectangular to Polar.

You are now looking at the south pole. Paint over the seams.
Now convert back to normal.

1. Go to Filter->Distort->Polar coordinates
2. Select Polar to Rectangular.

And finally, rescale your image back to it's original size.
The reason you scale it up, is because the polar transforms tend to reduce the resolution in some areas of the image, so that compensates for it. You now have an image which looks smudged along the top and bottom, but this is correct, because those areas will had been squeezed into a much smaller area. :beer:

Thanks for the step by step, tomot. I'd figured that Polar Coords distortion would be handy for the spherical backgrounds, but hadn't yet managed to get a full, clean pic.  Just what I needed. :)