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Mandelbrot 3D: Mandelnest

**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.

Linkback: https://fractalforums.org/index.php?topic=4028.0

**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 adition is classic.

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[0]); // convex form, or a0=acos(Z[0]) for concave dual form.

a1=asin(Z[1]);

a2=asin(Z[2]);

a0=P*a0;

a1=P*a1;

a2=P*a2;

M=pow(M,P);

Z[0]=sin(a0);

Z[1]=sin(a1);

Z[2]=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

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