Removing the discontinuities in the YZ-symmetrized 2nd-order Mandelbulbs

[msltoe]

Mircode: the copied parameter text worked for me. Make sure you are using the latest M3D v.1.6.8 code as he just added my formulas.

-mike

[Jesse]

It says "Error, formula option is not valid."
Doesn't this text configure the formula?
Which one do I have to select?

I can't find a way to enter the formula above, nor to translate the formula above to an m3f file...

Oh boy, I'm feeling like a stupid user. If I annoy you to much just let it be, I can understand it

Oh boy, what a stupid user 

kidding, just make sure to copy the whole text including mandelb... and the brackets, if it is still not working with program version 1.6.8 you have to specify the directory where the m3f formula files from the archive are stored in by clicking on the "INI DIRS" button + restart.
You should have a 'MsltoeSym2' formula in the formula window under '3D'.

[Mircode]

I configured everything via INI DIRS and restarted, still didnt work. But manually selecting Mstltoesym2 helped and I could finally render it.

http://dl.dropbox.com/u/11704339/MsltoeJuliaBig.png

[M Benesi]

The YZ symmetrized Juliabulbs I developed a long time ago (in 3-d fractal years) were only continuous with seeds (a,0,0). Recently, I figured out how to get continous (a,b,0) and (a,b,c), but the big price one pays is losing all of the spirals. Also, making the fractals continuous is not the same as making them smooth (= continuous derivatives), so they still look a bit fractured.
...
The code snippet for image 1:

   if (y*y<z*z) {d=y;y=z;z=d;}
   if (y>z) {x=-x;}
  
   r = x*x+y*y+z*z;
   x1 = (x*x-y*y)*(1-z*z/r);
   y1 =   (2*x*y)*(1-z*z/r);
   z1 =  2*z*sqrt(x*x+y*y);

   x=x1+a;y=y1+b;z=z1;

 I tried a slightly different approach a few months back, which resulted in a nice continuous (not in the derivative sense  ) fractal for z^2,6,10...:

  x1= (x*x-y*y-z*z);
  r=(x*x+y*y) ^ -.5;

  if (y>abs(z))
      { y1= 2* x * (y*y-z*z) *r }         else
      { y1 = - 2 * x * (y*y-z*z) *r }

  z1 =- 4 * x * y * z * r

  Didn't mess with julias of it too much however.