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Nice pic! - good colouring again. Do you know how similar this is to Rudy Rucker's formula? Here's an example pic I made a while back - some features seem similar:
http://www.skytopia.com/project/fractal/new/full/q30/RudyVines.jpg

I used the latest incarnation of my wip 3D formula for UF which I'm hoping to make available later this evening.
bib has been using a slightly earlier version since which I've further optimised and added some extra features.
Tonight I'll be adding the ability to colour using *any* UF outside colouring in UF5 - by simply performing the iteration for the surface pixels one extra time through UF's normal loop process - of course I'll have to add options as to how your 3D or 4D value is converted to a complex #z value to be passed to the colouring.

Oooops - I forgot to change the signature text in the PSP text tool

Here's the unoptimised non-trig UF code without analytical DE (non-trig as the trig code is left to the compiler):

                zjk = imag(zri) + flip(zj)
                r = cabs(zri)
                ph = cabs(zjk)
                if r>0.0
                  zri = (zri/r)^@mpwr ; cos sin
                else
                  zri = (1,0)
                endif
                if ph>0.0
                  zjk = (zjk/ph)^@mpwr ; cos sin
                else
                  zjk = (1,0)
                endif
                zj = imag(zjk)
                zri = real(zri) + flip(imag(zri)*real(zjk))
                x1 = sqrt(|zri| + sqr(zj))
                magn = magn^@mpwr
                if x1==0.0
                  zri = magn + cri
                  zj = cj
                else
                  magn = magn/x1
                  zri = magn*zri + cri
                  zj = magn*zj + cj
                endif
                magn = sqrt(|zri| + sqr(zj))

You may be wondering what that last bit with x1 is for, when recombining the sines/cosines using this method then the result does not have a fixed unit magnitude and rendering without the last "fix" produces a fractal that has spikes everywhere (essentially asymptotes) - it's interesting but I decided to see what happened if the combined sine/cosine result was renormalised before multiplication by the new magnitude.

Edit: If you want a name for the formula, I call it "Normalised simultaeneous rotation about z and x" or "Norm.Sim.Rot.ZX"