END OF AN ERA, FRACTALFORUMS.COM IS CONTINUED ON FRACTALFORUMS.ORG

// Gestaltlupe 3.4

double _scale=4;
double _offsetX=1.5;
double _offsetY=1.5;
double _offsetZ=1.5;
double _bailout=2;
double _angleX=0;
double _angleY=0;
double _angleZ=0;


public override void Init()
{
  base.Init();
  // Plaese remove this after pressing 2 times the button above:
  // (This set fixed formula Parameters)
  if(GetString("intern.Formula.TempUpdateVal")!="021462bd1ab1887e87f23a9ace4f4e0a")
  {
    SetParameterBulk(@"Formula.Parameters: angleX=0 angleY=0 angleZ=45 bailout=2 offsetX=2.1 offsetY=1 offsetZ=1 scale=2 Formula.Static: Cycles=12 Julia=1 jx=0.9 jy=0 jz=0 Scene: CenterX=0.0965003528449048 CenterY=-1.34226795790199 CenterZ=0.160980835845237 Radius=0.349530254720366 Transformation.Camera: AngleX=-39.2596575417366 AngleY=74.1173281658452 AngleZ=-99.2265259659284 IsometricProjection=0 Position=1 intern.Formula: TempUpdateVal=021462bd1ab1887e87f23a9ace4f4e0a");
  }

// Load current Parameters:
  _scale=GetOrSetDouble("scale");
  _offsetX=GetOrSetDouble("offsetX");
  _offsetY=GetOrSetDouble("offsetY");
  _offsetZ=GetOrSetDouble("offsetZ");
  _bailout=GetOrSetDouble("bailout");
  _angleX=Math.PI/180.0*GetOrSetDouble("angleX");
  _angleY=Math.PI/180.0*GetOrSetDouble("angleY");
  _angleZ=Math.PI/180.0*GetOrSetDouble("angleZ");
}
// Menger Sponge


public override bool GetBool(double x,double y,double z)
{
  // Switch between mandel and julia mode:
  double jx,jy,jz;
  if (_isJulia)
  {
    jx=_jx;
    jy=_jy;
    jz=_jz;
  }
  else
  {
    jx=x;
    jy=y;
    jz=z;
    x=_jx;
    y=_jy;
    z=_jz;
  }

  for (int n=1;n < _cycles;  n++)
  {

    // Menger Sponge Formula:
    x=Math.Abs(x);
    y=Math.Abs(y);
    z=Math.Abs(z);
    if(x>_bailout)return false;
    if(y>_bailout)return false;
    if(z>_bailout)return false;
    if (x<y)
    {
      double a=x;
      x=y;
      y=a;
    }
    if (x< z)
    {
      double a=x;
      x=z;
      z=a;
    }
    if (y<z)
    {
      double a=y;
      y=z;
      z=a;
    }
    x=_scale*x-_offsetX*(_scale-1);
    y=_scale*y-_offsetY*(_scale-1);
    z=_scale*z-_offsetZ*(_scale-1);
    if(z<-0.5*_offsetZ*(_scale-1.0))z+=_offsetZ*(_scale-1.0);
    if(_angleX!=0)Rotate(_angleX,ref y,ref z);
    if(_angleY!=0)Rotate(_angleY,ref x,ref z);
    if(_angleZ!=0)Rotate(_angleZ,ref x,ref y);
    // Julia / Mandel iteration:
    x+=jx;
    y+=jy;
    z+=jz;
  }
  return true;
}


void Rotate(double angle,ref double x,ref double y)
{
  double re=Math.Cos(angle );
  double im=Math.Sin(angle );
  double a=re * x-im * y;
  y=re * y+im * x;
  x=a;
}

angleX=0 angleY=0 angleZ=0
bailout=230 offsetX=1.05 offsetY=1 offsetZ=1
scale=2.2
Formula.Static: Cycles=16 Julia=1 jx=0.575 jy=0 jz=0

Some parameter variations:

<a href="https://www.youtube.com/v/RjTGNUG-yGY&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/RjTGNUG-yGY&rel=1&fs=1&hd=1</a>

Here you see a cut in the same Menger Sponge spiral. The green surface belongs to the "inside" while the grey very regular looking structures is an "outside view".

I found  a weird "i -1" in the code, how it got there I do not know.

This is what it should look like, (now I better go and fix the 4D version.)

A cut through one of the doughnuts.

I do not notice that Krzysztof Marczak has made 2013 a better version of my video in reply #4 .At minute 3:00 you see the broken picture frame of my first image. <a href="https://www.youtube.com/v/NIWz3BuE4nE&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/NIWz3BuE4nE&rel=1&fs=1&hd=1</a>

The only missing thing was a inner view of a menger sponge with 100 iterations, which seems to be unexplored.


Here is an outer view of the 45° menger sponge with a cut at z>0.

Formula.Parameters:
angleX=0 angleY=0 angleZ=45
bailout=6000000
offsetX=0.6 offsetY=2.8 offsetZ=0
scale=1.35
Formula.Static:
Cycles=75 Julia=1
jx=0.15 jy=0 jz=0

They are so good, so many different shapes (you can see where my last gallery post came from   thanks)