Just in case anyone's interested:

Here's a rotation of the z^2+c Mandy for this system:

http://www.fractalgallery.co.uk/EMF.mov

Also this multiplication table was inspired by the idea of any two of three perpendicular forces coming together producing a perpendicular result and is based on the obvious unit vector multiplication table for such a system, i.e.

   * |   r      i       j
   --------------------
   r  | +/-r  +/-j  +/-i
   i  | +/-j  +/-i  +/-r
   j  | +/-i  +/-r  +/-j

Obviously this gives 512 possibilities depending on the signs used - I tried a few and settled on one based on the fact that it was the most visually interesting Mandy