Something a hell of a lot easier is.. the complex triplex (from another post of mine elsewhere in the forums). It really makes the mathematical relationship to the original 2d set apparent:
You don't need anything too complex** to do triplex "algebra". You simply require:
A) a square root function to calculate a magnitude:
B) a complex power function:
complex_1= (x + i r1)^n
complex_2= (y + i z)^n
C) a real power function:
r3=r1^-n (you are applying the magnitude of y and z two times (once in each complex number), so need to divide it out once)
D) the ability to directly access the real and imaginary components of the complex numbers:
new x = real part of complex 1 + x pixel value OR x Julia seed (for Julias use the seed, Mandys use the pixel value)
new y = imaginary part of complex_1 * real part of complex 2 * r3 + y pixel value OR y Julia seed
new z = imaginary part of complex_1 * imaginary part of complex 2 * r3 + z pixel value OR z Julia seed
It's easily extended to higher dimensions... and is faster than the trig version in certain compilers (although I haven't tried them all).
** pun was and is still intended.... 2 complex.. although I didn't mention that it was intentional in the original post, as I felt it was a bit heavy handed to point out the pun. This, however, has changed.