Hi all, here's one based on bugman's latest suggestion, from here:

http://www.fractalforums.com/theory/3d-mandelbrot-formula-based-on-rotation-away-from-azimuthal-axis/

It's part of the z^8+c Mandelbrot.

"Theme Park Ride"



If no image above then look here:

http://makinmagic.deviantart.com/art/Theme-Park-Ride-146314193

very nice

Your colour choice really presents them in a nice way

On what are those colours based?

Also interesting shapes of course

so you basically colour it by a predefined gradient and the values to be used are the difference of true distance estimation and error?

Hmmm.... do you think, you could also try to color the set based on a spherical colour model?
(the center there is either black or white, so the brightness is either radius or inversed radius and the actual colour is given by the sign which gives the ratios of r,g,b...)

basically you start with colouring each point and then you just follow them without changing their specific colour... know what I mean?
So you could more or less graphically see where each point "came from"

Your current colouring technique is great too

This looks great! At first I didn't think this formula made very interesting looking Mandelbrots, but you've really added some nice flair to it.