Thank you Flexi. I will consider the Horner scheme for my Mandelbulb calculations although I feel that the number of iterations is not too important, actually I am working with an iteration depth of 7 only. The problem is when you go 3D you need an efficient algorithm to avoid having to calculate all points in the x,y,z space which would take ages. Some estimation/imterpolation is definitely required, and with the number of iterations this becomes more and more inefficient because the structures get "rougher" and cannot be reasonably interpolated.
I put the Mandelbulb to one side for the moment and focused on the Mandelbox. Got the algorithm working in principle to provide reasonably sharp pictures, and it's amazing. I never thought it was possible to travel through a 3D fractal in realtime, without weeks of rendering time. Got a bit stuck though with the rotation matrices and don't know how to have the preset manoever through the maze without running into the walls all the time. Hope to get that sorted soon.
