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 It seems that the standard juliabulb formula with the following "octahedral" transform leads to a sphereflake-like fractal.
 The Mandelbrot, version, as always, is not so pretty.

iterate on:

  if (x*x<y*y) {d=x;x=y;y=d;}
  if (y*y<z*z) {d=y;y=z;z=d;}
  if (x*x<z*z) {d=x;x=z;x=d;}

  <standard mandelbulb order 2>
  x=x-0.8; y=y;z=z;

and you get the following, which looks a lot like the sphereflake fractal, but not quite...

Beauty!

 

ASTOUNDING! Yeehaw, this is marvellous indeed