Fractal Flame using complex functions as conformal mappings

[tit_toinou]

Hi everyone.

Here is the list of typical variations functions of fractal flame :
http://code.google.com/p/flam3/wiki/Variations
They are to functions. We can understand them as functions that deforms the plane.

But what about using holomorphic (i.e. complex differentiable) functions ?
Has anyone ever tried to use them to render a flame fractal ?

I think they might be interesting as they can be use to do conformal mappings of the plane, where angles between two curves is conserved when the two curves are passed by the function (for images see http://fr.wikipedia.org/wiki/Transformation_conforme).
Plane deformations by theses kind of functions are aesthetically great because they turn infinitesimal squares into infinitesimal squares.

If no, can we implement our own functions in a software like Apophysis (or any other fractal flame software) ?
Thanks.