I used a simple distance formula:
D=SQR(M*M*3)
G=255/D*SQR(X*X+Y*Y+Z*Z)
GPSET DX,DY,RGB(G,G,G)
'When (0,0,0) is the back corner of the fractal and M is equal to the length, width, and height of the fractal.
I think your method is smart.
And I'd like to suggest another method.
All visible surfaces of the fractal can be divided into three groups of common normal vector, and you paint each of three groups in a different color.
When without perspective, we can regard the fractal on the screen as the aggregate of small regular hexagons separated by three colors.
Could you download [CECNN3RJ] and refer to "EX_MSPONGE" in the downloaded project?
Currently I have no idea with considering perspective.
Mandelbulb is like broccoli or butterbur sprout.
(This is off topic, but I love butterbur sprout tempura very much.)
I'd like to try to draw Mandelbulb. Now I'm looking for website which explains recursion formula of Mandelbulb.