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This 2nd order bulb is rotating around the j, i then real axes in turn. Just doing this is over-rotating the bulb, the surface area multiplies by 8 rather than by 4, so I fix this by putting the radius to the power of 2*sqrt(2).
It is interesting because 2 axes are symmetrical and 1 axis has rotational symmetry. It also shows 3d mandelbrot-like tendrils and looks to be connected. Still got whipped cream sections though

The code is:

              r = (magn=sqrt(magn))^(@mpwr*sqrt(@mpwr) - 1) ; the -1 because the rotated z is already scaled by mag before we multiply by r
              ; rotate around j
              th = @mpwr*atan2(zri)
              float flatJ = sqrt(|zri|)
              zri = flatJ*(cos(th) + flip(sin(th)))
              ; rotate around i
              float om = @mpwr*atan2(zj + flip(real(zri)))
              float flatI = sqrt(sqr(real(zri)) + sqr(zj))
              zj = flatI*cos(om)
              zri = (flatI*sin(om) + flip(imag(zri)))
              ; rotate around real
              ph = @mpwr*atan2(imag(zri) + flip(zj))
              float flatR = sqrt(sqr(imag(zri)) + sqr(zj))
              zj = flatR*sin(ph)
              zri = real(zri) + flip(flatR*cos(ph))

              zj = r*zj + cj
              zri = r*zri + cri