raising to a complex power?

[inhahe]

I heard that somewhere in these forum is a formula for raising the mandelbulb to a complex power, but I haven't been able to find it..
can somebody tell me what that formula is?
thx

[David Makin]

I heard that somewhere in these forum is a formula for raising the mandelbulb to a complex power, but I haven't been able to find it..
can somebody tell me what that formula is?
thx

http://www.fractalforums.com/3d-fractal-generation/true-3d-mandlebrot-type-fractal/msg8705/#msg8705

Note that that formula is the complex+real version of Paul Nylanders version of Daniel White's formula, not the version Daniel quotes in his skytopia article.

However I'm not sure how to get the derivative for the analytical distance estimate if you use fully complex powers - I've currently not actually tried non-real powers so at the moment for all my versions of the formula I'm just using the trig version of the derivative for real powers.

[kram1032]

I came to those results:

your new r = (r^2)^(x/2)
your new theta and phi = 2*pi*floor((-y log(r)-x phi+pi)/(2 pi))+y*log(r)+x*phi

with x+y*i being the complex exponent, r being the radius of your z and phi being the argument of it and phi being replacable by theta.
At least, that's true if I understood correctly, what happens with Mandelbulb...