@Jeannot Thank you, so kind of you! Will have a good look, hopefully tonight!

@3Dickulus  Have you changed anything? Because, honestly, to my best knowledge I have more often than not to get the parameters from a FragM-.png posted on here...
PS Hedgehoggie will have to wait till later too... Thank you for sharing, looks cool!

I tried another exotic norm for fun: norm(Z)= sqrt(abs(X)+abs(Y)+abs(Z))
(the vectors normalized by this pseudo-norm correspond to the surface of an octahedron and no longer the unit sphere or ordinary norm).
Julia power12 (asin-sin, Z0: -0.81, 0,0) gives a surprising result that I have never met with Mandelbrot 3D: it is hollow. Certainly a matter of filtering, the interior is not smooth. Above my modest steampunk style rendering 
The exact code I use untill now with my exotic norms: caution with the use of M or Me
   do
   {
             Me=sqrt( abs(Z[0])+abs(Z[1])+abs(Z[2]));//exotic Module Me 
             for(i=0;i<3;i++) Z/=Me; // exotic normalisation of new Z       -1<=x<=1
             a0=asin(Z[0]); // angles calculated with exotic Me
             a1=asin(Z[1]);
             a2=asin(Z[2]);
             a0=P*a0;
             a1=P*a1;
             a2=P*a2;
             M=pow(M,P);//Caution: here M is ordinary norm and not Me (possible to do with Me too)
             Z[0]=sin(a0);
             Z[1]=sin(a1);
             Z[2]=sin(a2);
             Z=normalize(Z,3); //Caution: ordinary normalization (possible to do with exotic Me too)
             for(i=0; i<3;i++) Z*=M;//Caution: ordinary norm here (possible with exotic Me too)
             Z=Z+C;
             M=norm(Z,3);//Caution: here ordinary norm for test and further pow (possible Me too)
             N++;
     }
          while((M<Mc) & (N<Maxit));         

@claude  abs(xyz) is abs(x*y*z) yes, but my interpretation (typo? due to lazy) is part of the exploration process

@Sabine62 if an image filename ends with .png then the server should not be altering it except when presenting a thumbnail so it should have parameters, as does Mr. Hedgehog image.

@Jeannot I find the evolution of something like this incredibly fascinating  takes on a life of it's own. The "standard" power for Mbulb is 8, I like to see the lower power versions to examine what lives there, Mbulb P2 displays the outline of the Mset etc.. the Mnest is a different animal still being explored, not sure if one can set a "standard" power... we'll see as it progresses

The non-Euclidean pseudo-norms associated with Mandelnest’s algorithm is a general method to provide many interesting variants.
The only constraint is to use a norm where components of the normed vector satisfy -1<=x<+1 (below an other exemple: draft of a cube-shaped fractal Modulus M= maxi (|x|, |y|, |z|)= Pnorm infinite. https://en.wikipedia.org/wiki/Lp_space#The_p-norm_in_finite_dimensions).
The P-norm is used at all levels of the code (calculation of angles, change to M^P and after the adition).
This cube is a borderline case difficult to edit: may be a good test for Fragmentarium...