Mandelbulb 2; interesting results at power 2

[TedWalther]

The mandelbulb is based on doing the following:

x = [1,0,0] y = [0,1,0] z = [0,0,1]
Take a 3d vector Z
rotate Z around z axis
rotate Z around x axis
double magnitude of Z
add a constant vector C

Mandelbulb2 is the same, but with one difference.  After the vector is rotated around the x axis, then also rotate the z axis by the same amount so that z, Z, and x are always in the same plane.

This way, a fresh new z axis is used in every iteration. The z axis will always be in the zy plane.

This produces the mandelbrot set for all Z,C pairs that are in the xy plane.  I believe this is the missing refinement to get a true 3d mandelbrot set.  I don't have time or resources to program it and visualize it.

Ted