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Mandelbrot 3D: Mandelnest

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Jeannot:
Hello
This family of 3D fractals has complete cubic symmetry (unlike Mandelbulb). Here images power 11.
Ever heard of it ? Already actually known ?
Otherwise I am available to provide the code to those who would like to improve the rendering.

There is à convex dual form.

Jeannot:
one convexe more

3DickUlus:
yess please :D code would be nice  :thumbs:

Jeannot:
Thanks. Here is the code.
The method is inspired by projective geometry (homogeneous coordinates), but it is very simple.
I use the usual Mandelbrot formula: Zn+1= Zn^p + c in space R3.
The multiplication in R3 is defined on the angles: at each iteration Zn is normalized and so we have for the 3 components -1<= x < =+1.
We can therefore naturally associate the 3 components with sines or cosines: x= cos(a0) and a0=acos(x).
Then classically Z^p is done by an+1= p x an and the module is increased to Mn+1= Mn^p.

Z=normalize(Z);
a0=asin(Z);  // convex form, or a0=acos(Z) for concave dual form.
a1=asin(Z);
a2=asin(Z);
a0=P*a0;
a1=P*a1;
a2=P*a2;
M=pow(M,P);

Z=sin(a0);
Z=sin(a1);
Z=sin(a2);
Z=normalize(Z);
for(int a=0; a<3;a++) Z[a]*=M;
Z=Z+C;
M=norm(Z);
N++;

Of course, the rendering can be significantly improved. I use my own graphics program openGL not very sophisticated.
Notice to candidates.
I take this opportunity to introduce myself: I am French (city of Poitiers), I am 61 years old and I have spent a lot of time trying to define a complex multiplication for R3, without of course achieving it  :,(

3DickUlus:
Thanks for sharing, this looks really interesting, I haven't seen this variation before.

edit: oh, and welcome to the forum :D