IMHO reason behind no 3D mandelbrot.

[Alef]

Few cutouts of different power brots and julia set. I named powers following n-square pattern. Square, cube, tesserct, penteract, hexeract, hepteract. Throught no octeract - 8 power.
https://sites.google.com/site/3dfractals/discussion

[Alef]

Finaly I got 8 power slonofractal formula.
Multiplication weren't so hard, stability calculations by Eurocodes is much more tought.
I got realy symmetric shape, what indicates that algebra should be correct, becouse in other formulas 8 power is the most symmetric and all accidental mistakes allways had led to distorted shapes. Alsou interesting inside render of fractal right at the center, place where in power 2 were mandelbrot shapes.

Formula, as expected, is extremely long:

Code:

zzx= zx^8 +8*zy^8 +210*zx^4*zy^8 -49*zx^6*szy^2 +8*zx^7*zz +28*zx^6*zz^2 -288*zx^5*zy^2*zz +56*zx^5*zz^3 -688*zx^4*zy^2*zz^2 +35*zx^4*zz^4 +800*zx^3*zy^4*zz -848*zx^3*zy^2*zz^3 +56*zx^3*zz^5 -140*zx^2*zy^6 +1004*zx^2*zy^4*zz^2 -418*zx^2*zy^2*zz^4 +28*zx^2*zz^6 -256*zx*zy^6*zz +480*zx*zy^4*zz^3 -178*zx*zy^2*zz^5 +8*zx*zz^7 -88*zy^6*zz^2 +68*zy^4*zz^4 -28*zy^2*zz^6 +Cx;

zzy= 224*zx^3*zy^5 -64*zx*zy^7 +8*zx^7*zy +56*zx^6*zy*zz -112*zx^5*zy^3 +168*zx^5*zy*zz^2 -560*zx^4*zy^3*zz +280*zx^4*zy*zz^3 -1064*zx^3*zy^3*zz^2 +280*zx^3*zy*zz^4 +672*zx^2*zy^5*zz -968*zx^2*zy^3*zz^3 +168*zx^2*zy*zz^5 +576*zx*zy^5*zz^2 -276*zx*zy^3*zz^4 +56*zx*zy*zz^6 -64*zy^7*zz +128*zy^5*zz^3 -66*zy^3*zz^5 +8*zy*zz^7 +Cy;

zzz= zz^8 +8*zy^ -84*zx^2*zy^6 -7*zx^6*zy^2 -48*zx^5*zy^*zz +70*zx^4*zy^4 -140*zx^4*zy^2*zz^2 +320*zx^3*zy^4*zz -224*zx^3*zy^2*zz^3 +516*zx^2*zy^4*zz^2 -210*zx^2*zy^2*zz^4 -192*zx*zy^6*zz +352*zx*zy^4*zz^3 +28*zx*zy^2*zz^5 -88*zy^6*zz^2 +68*zy^4*zz^4 -18*zy^2*zz^6 +abs(Cz);

zx= zzx;
zy= zzy;
zz= abs(zzz);

Wiev from the top (z axis)



Wiev from the side:



Cutout somewhere along z=-0.2. Inside of it are more mandelbrot features than outdide wiev suggest. Top wiev:



Julia set, side wiev:



Inside render in somewhere about the center of  slonofractal. I got this just zooming in from top wiev:


p.s.
The same here https://sites.google.com/site/3dfractals/discussion

[Alef]

Good quality pic of power 2 fractal.

[jehovajah]

Very nice! We ought to expect the 3d version to look rough, after all, diamonds do until cut and polished!