### JosLeys Kleinian Group Variations

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#### trafassel #### JosLeys Kleinian Group Variations

« on: September 12, 2018, 03:08:29 AM »
Linear line of separation and extended folding.

// Gestaltlupe Formula:
public double LOSx=0;
public double LOSy=0;
public double KleinR;
public double KleinI;
public double minBailout;
public bool useLineOfSeparation;
public double losXScale;
public double losYScale;
public bool classicFolding;
public double zs;
public override bool GetBool(double x,double y,double z)
{
double losXScaleFactor=losXScale*2.0*Math.PI;
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 i=0;i < _cycles;  i++)
{
if(classicFolding)
{
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;
}
}
else
{
x=x-Math.Floor(x+0.5);
z=z-Math.Floor(z+0.5);
}
if(useLineOfSeparation)
{
if (y >=LOSy+KleinR*(0.5+losYScale*(x)))
{
x=KleinI-x;
y=KleinR-y;
z=-zs*z;
}
}
double xx=x*x,yy=y*y,zz=z*z;
double r=xx+yy+zz;
if(r>0)
{
x /=r;
y /=r;
z /=r;
if(r>0.00000000001 && i>2)
{
Red+=xx/r;
Green+=yy/r;
Blue+=zz/r;
}
if(r<minBailout)return false;
}
x=KleinI+x;
y=KleinR-y;
z=-z;
x+=jx;
y+=jy;
z+=jz;
}
return true;
}

public override void Init()
{
base.Init();
if(GetString("intern.Formula.TempUpdateVal")!="789aa147972a8a558d25a6b7e4d210fa")
{
SetParameterBulk("Formula.Parameters: classicFolding=1 KleinI=0.009828904647462 KleinR=1.95409610447188 LOSx=0 losXScale=0 LOSy=0.3 losYScale=-0.6 minBailout=0.3 useLineOfSeparation=1 zs=-1 Formula.Static: Cycles=99 Julia=1 jx=0.026 jy=-0.022 jz=0 Scene: CenterX=5.73474421250101 CenterY=1.0959603439525 CenterZ=-3.10428195727539 Radius=0.0509876305851325 Transformation.Camera: AngleX=111.889205636214 AngleY=7.89161900064529 AngleZ=172.783555796052 IsometricProjection=0 Position=1 intern.Formula: TempUpdateVal=789aa147972a8a558d25a6b7e4d210fa");
}
}

#### trafassel #### Re: JosLeys Kleinian Group Variations

« Reply #1 on: September 16, 2018, 01:24:01 AM »
Same formula, but with less parameters.

public double LOSy=0;
public double KleinR;
public double KleinI;
public double minBailout;
public bool useLineOfSeparation;
public double losYScale;
// Escape time algorithm for Kleinian group limit sets from JosLeys and Knighty.
// http://www.fractalforums.com/index.php?topic=24728.0
public override bool GetBool(double x, double y, double z)
{
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 i = 0;i < _cycles;  i++)
{
x=x%2;
z=z%2;
while(Math.Abs(x)>0.5)
{
if(x>0) x = 1-x;
else x = -1-x;
}
while(Math.Abs(z)>0.5)
{
if(z>0) z = 1-z;
else z = -1-z;
}
if(useLineOfSeparation)
{
if ( y >= LOSy+losYScale*x)
{
x = KleinI-x;
y = KleinR-y;
}
}
double xx=x*x,yy=y*y,zz=z*z;
double r=xx+yy+zz;
if(r>0)
{
x /= r;
y /= r;
z /= r;
if(r>0.00000000001 && i>2)
{
Red+=xx/r;
Green+=yy/r;
Blue+=zz/r;
}
if(r<minBailout) return false;
}
y = - y;
z = -z;
x+= jx;
y+= jy;
z+= jz;
}
return true;
}

// Parameters

public override void Init()
{
base.Init();
if(GetString("intern.Formula.TempUpdateVal")!="e8b0b60bb63ce0251b91632bd6a7111e")
{
SetParameterBulk("Formula.Parameters: KleinI=0.009828904647462 KleinR=1.95409610447188 LOSy=1.061 losYScale=-0.23 minBailout=0.26 useLineOfSeparation=1 Formula.Static: Cycles=99 Julia=1 jx=0.035828904647462 jy=1.93209610447188 jz=0 Scene: CenterX=6.10045210856169 CenterY=0.829893641423711 CenterZ=-4.00931033080474 Radius=3.47612962004208E-05 Transformation.Camera: AngleX=-165.661479864796 AngleY=21.2063977841397 AngleZ=113.770236935814 IsometricProjection=0 Position=1 intern.Formula: TempUpdateVal=e8b0b60bb63ce0251b91632bd6a7111e");
}
}

#### pauldelbrot #### Re: JosLeys Kleinian Group Variations

« Reply #2 on: September 16, 2018, 08:57:55 AM »
O.o

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