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The function is

 r=x*x+y*y+z*z
 x1 = (x*x-y*y)*(1-z*z/r)
 y1 = 2*x*y*(1-z*z/r)
 z1 = 2*z*sqrt(r)
 x=x1+a;y=y1+b;z=z1+c;

The domain (r < threshold) is the spherical neighborhood of the root.
You can color it completely (to make spherical roots) or you can do something more fancy
like render torii:

It's slightly different from true escape-time in that when r < threshold, I terminate the loop as I've now reached the neighborhood of a root.
The root is presumably at x=0,y=0,z=0. With that assumption I can draw things with respect to that origin.
The torus, for example, is defined as points that are within a certain distance of a circle centered at the presumed origin.

Uhm, second that... great work as always msltoe! Looks lovely

Back to compiling formulas Luca!!!