END OF AN ERA, FRACTALFORUMS.COM IS CONTINUED ON FRACTALFORUMS.ORG

  Do you mean to:

theta= acos [(y + i*z) / h]
phi=    asin [(x + i*z) / h]

  with the regular arccos/arcsin functions?

Another point is that the above gives us a trilplex form than can be extended upward to R4,R5,R6.....Rn using a similar method - unlike the quaternion and hypercomplex methods which only give us Rn where n=2^x (x integer >=2).

Just tried the 4D version i.e. a complex angle plus complex pythagoras - it's most definitely *not* an alternative way of describing standard bicomplex.
It wasn't that interesting until I started playing with the signs - I suggest folks so inclined try this 4D version of z^2+c, obviously just convert the complex calculations into the real equivalents if you don't have complex as a type.

      r = x*x + y*y + z*z + w*w
      complex xy = x + flip(y)
      complex zw = z + flip(w)
      complex ccs = 1.0/sqrt(sqr(conj(xy)) + sqr(conj(zw)))
      complex csn = zw*ccs
      ccs = xy*ccs
      xy = r*(sqr(ccs)-sqr(csn))
      zw = 2.0*r*ccs*csn
      x = real(xy) + cx
      y = imag(xy) + cy
      z = real(zw) + cz
      w = imag(zw) + cw

For DE the standard method for quaternionic z^2+c should work OK.
I just rendered it using my really old UF code (in mmf.ufm) so it's not worth posting one of my own renders at the moment.
It's very reminiscent of the Mandelbar but in 3D, so I think further investigations into variations on the theme may prove fruitful