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Hi, sorry, with my program I generated this set of high 3d mandel to the second power. What do you think? Thank you in advance

Good! Bravo!  :dink:
Formula used?! :beer:

Hi, I used the following formula, but since i'm not a math I have doubts about nw. I attach pictures with other angles

            case 14:
               rad = Math::Sqrt(nx*nx + ny*ny + nz*nz + nw*nw);

               powRad = Math::Pow(rad, power);
               theta = Math::Atan2(ny, nx) * power;
               phi = Math::Atan(nz / rad) * power;
               nx = powRad * Math::Cos(theta) * Math::Cos(phi);
               ny = powRad * Math::Sin(theta) * Math::Cos(phi);
               nz = powRad * Math::Sin(phi) * inverse_azimuth;
               nw = powRad * Math::Sin(phi) * inverse_azimuth;
               break;

            default:
               break;
            }

            if(julia)
            {
               nx += creal_i;
               ny += cimag_j;
               nz += k;
               nw += l;
            }
            else
            {
               nx += x;
               ny += y;
               nz += z;
            }

This is the corresponding collection of julia

A screen of my program

Julia set with k and l values ​​automatically calculated

It's good but this one looks more like 3D http://www.fractalforums.com/the-3d-mandelbulb/true-3d-mandelbrot/ (http://www.fractalforums.com/the-3d-mandelbulb/true-3d-mandelbrot/)

Your in zoom probably will reveal mandelbrotesque features, but there is nothing on its top.

Thank you Alef, thanks to all of you, it is a great satisfaction for me

I replied with the OpenTK

Hello, I replied with Mandlbulb3Dv191.
Formula used:

procedure MyFormula(var x, y, z, w: Double; PIteration3D: TPIteration3D);
var
   sq_r: double;
   sq_xz: double;
   r, theta, zangle: double;
begin
   sq_r := sqrt(x*x+y*y+z*z);
   sq_xz := sqrt(x*x+z*z);
   r:= power(sq_r, Power_);

   theta := arctan2(y , x) * Power_;
   zangle := arctan2(z, sq_r) * Power_;

   x := cos(zangle) * cos(theta)  * r + PIteration3D^.J1;
   y := sin(theta)  * cos(zangle) * r + PIteration3D^.J2;
   z := sin(zangle) * r * inverse     + PIteration3D^.J3;
end;

Mandel:
     inverse = 1

Julia:
     inverse = -1

To the third power

Elevated to the power of 4 and top view

Power 5 and left view

Power 8 Julia

Top View

Mandelbulb3Dv191 has detected more details. Thank you

Julia 3d / 2d comparison

Julia values ​​used

Julia 3d / 2d comparison

It reminds me Quat software. Is it similar?

I really can not answer your question, but the comparison can do the same to you.

My program works like this:

The main class is called Fractals where there are all functions for 2d / 3d calculation
and is derived from AllParam where there are all variables, arrays, Bitmaps etc. used in the program.
In a function I populated a class Fractals instance with values coming from other structures.
The main feature is that each FormChild is a key / value dictionary, or, to put it better,
each FormChild has a key / value dictionary associated.
The key is the child name (childName), the value is an instance of the Fractals class (fractals).
Once calculated, the image is stored in the bitmapBase variable contained in AllParam.
So once you've created the image, you do not have to recalculate it.
FormChilds can be closed, resized, moved, etc., but nothing is lost.
In the History menu on the right, just double click to reload the parameters and then
click on the Draw button, where there is a dedicated if statement, to reload the image in memory.
For each Form I have created a structure with default values.
Structures are instantiated in associated forms, and parameter changes in forms,
they actually change the values of the associated structure.
Each time a FormChild is activated, a delegated function is called,
which will update all the parameters. Other than that.

As far as the program is concerned, I manage it and do it for hobby and entertainment,
and I honestly never thought of publishing it, also because I have to review and add different
functionality (parallelization, testing, etc.).

Thank you

With the following formula we get the following images. Respectively power = 2 and power = 4

powRad = Math::Pow(rad, power);
theta = Math::Atan2(ny, nx) * power;
phi = Math::Atan2(nz, rad) * power;
nx = powRad * (2.0 / (Math::Exp(phi) + Math::Exp(-phi))) * Math::Cos(theta); //Sech(phi)
ny = powRad * (2.0 / (Math::Exp(phi) + Math::Exp(-phi))) * Math::Sin(theta);
nz = powRad * Math::Tanh(phi) * inverse_azimuth;
nw = powRad * Math::Tanh(phi) * inverse_azimuth;

Self similarity, power = 2

              Minimum                      Maximum
X  -0,179966626034698     -0,136156134732695
Y  -1,06056022828191       -0,995683067492954

Julia, X axis rotation: degrees = 35, power = 2

Wow, looks great!

Thank you, thank you so much

Julia, power = 2

Julia, power = 2

five

Comparison. No zoom, the coordinates are identical

            if(julia)
            {
               nx += creal_i;
               ny += cimag_j;
               nz += k;
               nw += l;
               nm += m;
            }
            else
            {
               nx += x + x;
               ny += y + y;
               nz += z + z;
            }

Do you need to insert the formula inside the software code or it has a function to run it?

Yes, what you see is extracted from a function

Thank you

six

six, Julia black marker

six, Julia darkred marker