HI all, This is a question relating to the elusive "holy grail" of a perfect Mandelbrot Set in 3D. As I understand it the problems with respect to getting "whipped cream" in non-linear pure-3D fractals is related to the facts that there are no complete algebraic fields in R3 and that (by Louiville's (conformality) theorem) conformal mappings are restricted to mobius transforms only. With respect to Louiville's theorem: http://en.wikipedia.org/wiki/Liouville%27s_theorem_%28conformal_mappings%29 The proof shows that any Rn (n>2) mapping/transform that is not a mobius transform will not be conformal. My question (due to my own ignorance/lack of understanding) is: Does Louiville's theorem also discount the possibility of an Rn non-mobius mapping/transform being conformal in Rx space (x<n) if only Rx of the Rn space is considered ? For example is it not possible that if we have Rn (n>3) then a non-Mobius mapping/transform in Rn could be such that all non-conformality is restricted to a particular Rx of Rn where x>=1 and x<n-2 ? If so then I think the holy grail 3D Mandelbrot view is still a possibility albeit with the actual algebra being Ry (y>3). Please forgive me if I sound completely ignorant or totally insane :) Or if you don't think this is "math fun" ;) bye Dave