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Mandelbrot Spiral In 3DMandelbulb PlantEnergy Core In A Stellarator Design
Mandelbulb Plant
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Description: My first spirals in a power 2 Mandelbulb variant.
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Filesize: 246kB
Height: 1092 Width: 1200
Discussion Topic: View Topic
Keywords: Mandelbulb Gestaltlupe 
Posted by: trafassel February 29, 2016, 10:48:10 PM

Rating: ***** by 4 members.

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KRAFTWERK
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March 01, 2016, 08:36:36 PM
WOW, spirals upon spirals  roll eyes, never seen anything like this.
Great find Trafassel!  A Beer Cup
Tater
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March 01, 2016, 06:14:30 AM
Thanks a lot. Looking forward to seeing improvements.
trafassel
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March 01, 2016, 12:05:27 AM
Yes no problem, but i dont't think, that the formula is 'ready'. The overview of the 3D Mandelbrot form has still some ugly areas.

The formula is a power 2 Sinus Mandebulb variant. Short form:

Number of iterations: _cycles=256
Bailout: gr=20
br,bi,bj are the (x,y,z) components of the 3d point to test.


for (int n=1;n < _cycles;  n++)
  {
    double phi=Math.Atan2(y,x);
    double x1=x;
    x=Math.Cos(-phi)* x-Math.Sin(-phi)* y;
    y=0;
    theta=Math.Atan2(-z,-x);
    if(spin)
    {
      theta=theta+Math.PI;
    }
    theta=(_power-1)*theta;
    double x2=x;
    re=Math.Cos(theta );
    im=Math.Sin(theta );
    a=re * x-im * z;
    z=re * z+im * x;
    x=a;
    if(x2*x<0)spin=!spin;
    re=Math.Cos(_power*phi);
    im=Math.Sin(_power*phi);
    a=re * x-im * y;
    y=re * y+im * x;
    x=a;
    xx=x * x;
    yy=y * y;
    zz=z * z;
    r=xx+yy+zz;
    r=Math.Pow(r,(_power-1)/2);
    x *=r;
    y *=r;
    z *=r;
    y+=bj;
    x+=br;
    z+=bi;
    if (r > gr)return false;
}
return (true);



The compressed formula (for Gestaltupe 3.2 available at www.gestaltlupe.com). You have to paste it in the formula tab.

int gr=20;double _power=2;bool _sinusVariant=false;bool _bulbVariant=false;public override void Init(){base.Init();if(GetString("intern.Formula.TempUpdateVal")!="57b771cfb8c1c0ed8f5782be552073a4"){SetParameterBulk("Formula.Parameters: BulbVariant=0 Power=2 SinusVariant=0 Formula.Static: Cycles=256 Julia=0 jx=0 jy=0 jz=0 Scene: CenterX=0.278416265799056 CenterY=9.50816239684936E-05 CenterZ=0.0103610297255821 Radius=0.00018314136519529 Transformation.Camera: AngleX=-161.234448298483 AngleY=-9.47833617990776 AngleZ=-176.797675777867 IsometricProjection=0 Position=1 intern.Formula: TempUpdateVal=57b771cfb8c1c0ed8f5782be552073a4");}_power=GetOrSetDouble("Power",2,"Mandelbulb Power.");if(!Fractrace.Basic.ParameterDict.Current.Exists("Formula.Parameters.SinusVariant")){Fractrace.Basic.ParameterDict.Current["Formula.Parameters.SinusVariant"]="0";}_sinusVariant=Fractrace.Basic.ParameterDict.Current.GetBool ("Formula.Parameters.SinusVariant");if(!Fractrace.Basic.ParameterDict.Current.Exists("Formula.Parameters.BulbVariant")){Fractrace.Basic.ParameterDict.Current["Formula.Parameters.BulbVariant"]="0";}_bulbVariant=Fractrace.Basic.ParameterDict.Current.GetBool ("Formula.Parameters.BulbVariant");Fractrace.Basic.ParameterDict.Current["Formula.Parameters.SinusVariant.PARAMETERINFO.Datatype"]="Bool";Fractrace.Basic.ParameterDict.Current["Formula.Parameters.BulbVariant.PARAMETERINFO.Datatype"]="Bool";}public override bool GetBool(double x,double y,double z){double br,bi,bj;if (_isJulia){br=_jx;bi=_jy;bj=_jz;}else{br=x;bi=y;bj=z;x=_jx;y=_jy;z=_jz;}double xx=x * x;double yy=y * y;double zz=z * z;double r=0;double re=0,im=0,a=0;double theta=0;bool spin=false;for (int n=1;n < _cycles;n++){double phi=Math.Atan2(y,x);double x1=x;x=Math.Cos(-phi)* x-Math.Sin(-phi)* y;y=0;if(_sinusVariant)theta=Math.Atan2(z,x);else theta=Math.Atan2(-z,-x);if(_bulbVariant && n==2 )theta=Math.PI-theta;if(spin){theta=theta+Math.PI;}theta=(_power-1)*theta;double x2=x;re=Math.Cos(theta );im=Math.Sin(theta );a=re * x-im * z;z=re * z+im * x;x=a;if(x2*x<0)spin=!spin;re=Math.Cos(_power*phi);im=Math.Sin(_power*phi);a=re * x-im * y;y=re * y+im * x;x=a;xx=x * x;yy=y * y;zz=z * z;r=xx+yy+zz;r=Math.Pow(r,(_power-1)/2);x *=r;y *=r;z *=r;y+=bj;x+=br;z+=bi;if (r > gr)return false;if (n > _cycles/ 3 && n < _cycles/ 1.2){additionalPointInfo.red+=xx / r;additionalPointInfo.green+=yy / r;additionalPointInfo.blue+=zz / r;}}return (true);}



Tater
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February 29, 2016, 11:19:33 PM
Interesting. Can you share the code?

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