Maybe a Fish eye transform

[Alef]

3D fractal world looks simmilar to photography. In both you have to consider lights, shadows, you can use focal lenght (DOF) to accentuate certain object and smooth outh background.

But you can alsou put Fish Eye lenses.

You can modifie pixel maping by complex sigmoid function like z=((2+cabs(pixel) )/3)*pixel;
or in 3D space you can use this conformal vector transformation (position dependant scaling) of a shape:

fisheye=(1+sqrt(zx^2+zy^2+zz^2) )/2;
zx=fisheye*zx;
zy=fisheye*zy;
zz=fisheye*zz;

But then you lose fog/ lights and shadows of "Fish Eye" and it is just a mere aproximation.


http://en.wikipedia.org/wiki/Fisheye_lens

[taurus]

Buddhi implemented a simulation of a fisheye-lens in mandelbulber since very early versions. as far as i see, you loose neither fog, nor light or shadow.
mandelbulber is open source, so everyone can comprehend how he did this...

[PhotoComix]

may be possible solve without reinventing the wheel ?

I used often a cool Open Source program called "Panini" (from the name of a Italian painter known for his peculiar use of prospective )
http://sourceforge.net/projects/pvqt/
 that  could apply and convert from /to a lot of different types type of "mapping" (Panini be just one of many that may be applied )

And obviouslys contain all the formula for the most commune, and in some case even less commune types of conformal and not conformal mappings