I added a new formula to mandelbulber with the following code in fractals.cpp
double newx = 2.0*z.y*z.z;
double newy = - 0.8*z.x*z.x - 1.2*z.x*z.y + 0.8*z.y*z.y - 0.8*z.z*z.z;
double newz = - 0.6*z.x*z.x + 1.6*z.x*z.y + 0.6*z.y*z.y - 0.6*z.z*z.z;
z.x = newx + constant.x;
z.y = newy + constant.y;
z.z = newz + constant.z;
r = z.Length();
A friend of mine used this changed mandelbulber code to make a short video of the resulting fractal.
As you can see the resulting fractal changes it's shape when you zoom in, I wonder if this is known behaviour cause of the way mandelbulber works, or if I missed something in adding the formula. Any suggestions to make these zooming changes disapear are welcome.
Generally it's an interesting formula. I have just tested it.
Some small changes of shape are caused by changing of detail level during zooming in. It is because there is implemented dynamic distance threshold (DE algorithm is used). If you want to avoid changing of the shape you can switch on "Const. DE threshold" and put DE threshold value manually. But then during zooming you will not see more detail or you will have to much detail when it will be zoomed out (visible aliasing and noise).