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News from the MandelboxMandelbox Julia with SpiralsThe Pocket Watch of my Grandpa
Mandelbox Julia with Spirals
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Description:  // Mandelbox Julia with fold at 0.5, scale = 1 and without y transformation.
// CenterX=5.50297045220822 CenterY=0.583399182382745
// CenterZ=2.10738023707053 Radius=0.214958267491292
public override bool GetBool(double x, double y, double z)
{
  for (int i = 0;i < 77;  i++)
  {
      while(Math.Abs(x)>0.5)
      {
        while(x>0.5)  x =  1-x;
        while(x<-0.5) x = -1-x;
      }
      while(Math.Abs(z)>0.5)
      {
        while(z>0.5)  z =  1-z;
        while(z<-0.5) z = -1-z;
      }
    double r=x*x+y*y+z*z;
    if(r>0)
    {
      x /= r;
      y /= r;
      z /= r;
      if(r<0.3) return false;
    }
    y=-y;
    x+= 0.02;
    y+= 1.9;
    z+= 0.5;
  }
  return true;
}

Stats:
Total Favorities: 0 View Who Favorited
Filesize: 248.26kB
Height: 1159 Width: 1200
Discussion Topic: View Topic
Keywords: Mandelbox Spiral Gestaltlupe 
Posted by: trafassel January 09, 2017, 01:12:17 AM

Rating: ***** by 2 members.

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  Slideshow  

Comments (4) rss
trafassel
Fractal Bachius
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Posts: 531


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January 09, 2017, 11:35:29 PM
Thanx pupukuusikko.

I did not test other scales than 1.

The idea of using box size of 0.5 to reach nice results for scaling 1 comes from msltoe (see: http://www.fractalforums.com/index.php?action=gallery;sa=view;id=7604).

Set x=-x in each iteration is inspired from the escape time algorithm for Kleinian group limit sets fragment code at http://www.fractalforums.com/3d-fractal-generation/an-escape-tim-algorithm-for-kleinian-group-limit-sets/msg98248/#msg98248 .

Using unlimited folding as demostrated here and remove y folding makes the spirals more regular. This ideas was also inspired from the Kleinian Group formula by trying to remove the cuts, caused by the line of separation.

I.e. the unlimited folding is of course much faster, if you use:

      x=x%2;
      z=z%2;
      while(Math.Abs(x)>0.5)
      {
        if(x>0.5)  x =  1-x;
        if(x<-0.5) x = -1-x;
      }
      while(Math.Abs(z)>0.5)
      {
        if(z>0.5)  z =  1-z;
        if(z<-0.5) z = -1-z;
      }

This is not the same as:

      x = x-Math.Floor(x+0.5);
      z = z-Math.Floor(z+0.5);

which is used in the escape time algorithm for Kleinian Group.

Although there is no y folding the fractal is not flat as expected and the spirals occour in all 3D directions.



pupukuusikko
Alien
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Posts: 35


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January 09, 2017, 07:40:55 PM
Excellent spirals. A Beer Cup How does the brot look without folding on y axis?
Do you see spirals on more reasonable scales? As you know, with DE methods
approaching scale=1.0 is difficult.
trafassel
Fractal Bachius
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Posts: 531


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January 09, 2017, 10:52:23 AM
Thank you. I newer know, that generating spirals in the Mandelbox was so simple.
mclarekin
Fractal Senior
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Posts: 1739



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January 09, 2017, 03:47:31 AM
Nice one afro afro afro

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