One of reason for making my Ultra Fractal / Chaos Pro buddhabrot were to make model for a buddhabrot software as most of encountered buddhabrot renderers were pretty featurless. I can list what buddhabrot soft don't have. In implementing it I went away from buddhabrots so to make it faster and more accesible at the extent that it's hardly should be called a buddhabrot. Throught some of my renders pops up when you google search for budhabrot with single d, that could something to do with my poor english.
Number of things I did should work with proper buddhabrots. Implementing it as hack in fractal generator and wieving buddhabrot method as module based eased the experimentation.
At first I tested some hundreds of formulas I know or found in UF or Fractint's orgform (and took some from Kram and one guy sharing Fractints videos) and so far picked 31, throught not all of them are equaly good but I would recomend at least quadratic general, eye, logic turtle and changable power for mandelbrot. Some escape time formulas don't work as orbit plots but some have amazing orbit plots even with boring mandelbrot sets. All dedicated buddhabrot renderers have just one formula and that's quite a boring. IMHO these formulas should work for any buddhabrot just some pobably would need to be converted to non-complex numbers.
Second, even with many formulas image variance is limited, and it's not so zoomable, and then it don't have julia sets. Trying different combinations I found "quasi julia sets" generating much more variance, and even slightly zoomable as some small parts have interesting fractal shapes. It could work with normal buddhabrots, throught I never picked escaping / non escaping orbits.
Third, If you have RGB colour values, you can switch them in places, invert or apply many transfer functions. All will work on any (0<rgab values<1) RGB colour methods including buddhabrots. What the point to render same coloured images again and again.
Fourth, buddhabrots often are equaliset by white balance. Sigmoid function were great at downregulating equalisation and it kind of made equalistaion softer.
Here (but my image sharing site is down):
http://www.fractalforums.com/fractal-programs/problems-with-implementing-budhabrot-in-uf/msg62482/