### Fake 3D Mandelbrot Set

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#### trafassel

• Fractal Friend
• Posts: 16

#### Fake 3D Mandelbrot Set

« on: August 30, 2018, 10:17:30 PM »
Because the search for the real 3D Mandelbrot Set ist frustrating, I start to create some fake 3D Mandelbrot Fractals by disturbing the Mandelbrot Set with the parameter z.

All Formulas are Gestaltlupe fomulas.

Code: [Select]
public double minr;public int maxi;public double scale1;public double scale2;public double scale3;public bool usecolors;public double mrscale;public double scale1m;public double z1;double jx,jy,jz;public override bool GetBool(double x,double y,double z){  if (_isJulia)  {    jx=_jx;    jy=_jy;    jz=_jz;  }  else  {    jx=x;    jy=y;    jz=z;    x=_jx;    y=_jy;    z=_jz;  }  Red=0;  Green=0;  Blue=0;  double mr=minr;  double s1=scale1;  for (int i=1;i<_cycles;  i++)  {    double xx=x*x;    double yy=y*y;    double zz=z*z;    double r=xx+yy+scale3*zz;    if (r>6)return false;    if(r>0)    {      Red+=xx/r;      Green+=yy/r;      Blue+=zz/r;    }    mr*=mrscale;    s1*=scale1m;    if (r<mr && i>maxi)    {      return true;    }    y=2*x*y+jy;    x=xx-yy+z1*zz+jx;    z=s1*z*Math.Pow(r,scale2)+jz;  }  return true;}public override void Init(){  base.Init();  if(GetString("intern.Formula.TempUpdateVal")!="cbc1199bac7a0e477ce6112cfcbb05b7")  {    SetParameterBulk("Formula.Parameters: maxi=22 minr=4E-07 mrscale=1.27 scale1=1.61 scale1m=1.005 scale2=0.461 scale3=0.2 usecolors=0 z1=3 Formula.Static: Cycles=399 Julia=0 jx=0 jy=0 jz=0 Scene: CenterX=0.360349307269346 CenterY=-0.0896839428186666 CenterZ=0.000907168580142697 Radius=0.00239437249839199 Transformation.Camera: AngleX=12.6034368774674 AngleY=-40.6311848461177 AngleZ=-31.5578735989771 IsometricProjection=0 Position=1 intern.Formula: TempUpdateVal=cbc1199bac7a0e477ce6112cfcbb05b7");  }}

#### trafassel

• Fractal Friend
• Posts: 16

#### Re: Fake 3D Mandelbrot Set

« Reply #1 on: August 30, 2018, 10:27:23 PM »
An inside view.

Code: [Select]
 public override void Init(){base.Init();if(GetString("intern.Formula.TempUpdateVal")!="a3efa36bb785d574f75d0e896ce97532"){SetParameterBulk("Formula.Parameters: maxi=222 minr=0.041 mrscale=1 scale1=1.572 scale1m=1.004 scale2=0.461 scale3=0.2 scalez=0.3 usecolors=0 z1=44 z4=0.99 Formula.Static: Cycles=555 Julia=0 jx=0 jy=0 jz=0 Scene: CenterX=-0.747347029826688 CenterY=-0.110663797335455 CenterZ=-0.000147633958289673 Radius=0.000263105188884941 Transformation.Camera: AngleX=-91.4661284939803 AngleY=18.5279605112074 AngleZ=-29.1587133688556 IsometricProjection=0 Position=1 intern.Formula: TempUpdateVal=a3efa36bb785d574f75d0e896ce97532");}}public double minr=0.05;public int maxi=17;public double scale1=2;public double scale2=0.5;public double scale3=0.5;public bool usecolors=true;public double mrscale=0.99;public double scale1m=1;public double z1=0;double jx,jy,jz;public double scalez=1;public double z4=1;public override bool GetBool(double x,double y,double z){if(z<0){}else z=Math.Pow(z,z4);z*=scalez;if (_isJulia){jx=_jx;jy=_jy;jz=_jz;}else{jx=x;jy=y;jz=z;x=_jx;y=_jy;z=_jz;}Red=0;Green=0;Blue=0;double mr=minr;double s1=scale1;double z3=scalez;for (int i=1;i<_cycles;i++){z3*=z4;double xx=x*x;double yy=y*y;double zz=z*z;double r=xx+yy+scale3*zz;if(r>0){Red+=xx/r;Green+=yy/r;Blue+=zz/r;}if (r>6)return false;mr*=mrscale;s1*=scale1m;if (r<mr && i>maxi){return true;}y=2*x*y+jy;x=xx-yy+z1*zz+jx;z=s1*z*Math.Pow(r,scale2)+jz;}return true;}

#### Sabine62

• Fractal Frankfurter
• Posts: 572

#### Re: Fake 3D Mandelbrot Set

« Reply #2 on: August 31, 2018, 09:05:16 AM »
Really nice looking results, fake or not
To thine own self be true

#### trafassel

• Fractal Friend
• Posts: 16

#### Re: Fake 3D Mandelbrot Set

« Reply #3 on: August 31, 2018, 07:56:00 PM »
Thanks.

Code: [Select]
public double minr=0.05;public int maxi=17;public double scale1=2;public double scale2=0.5;public double scale3=0.5;public bool usecolors=true;public double mrscale=0.99;public double scale1m=1;public double z1=0;double jx,jy,jz;public double scalez=1;public double z4=1;public override bool GetBool(double x,double y,double z){  if(z<0)  {  }  else z=Math.Pow(z,z4);  z*=scalez;  if (_isJulia)  {    jx=_jx;    jy=_jy;    jz=_jz;  }  else  {    jx=x;    jy=y;    jz=z;    x=_jx;    y=_jy;    z=_jz;  }  Red=0;  Green=0;  Blue=0;  double mr=minr;  double s1=scale1;  double z3=scalez;  for (int i=1;i<_cycles;  i++)  {    z3*=z4;    double xx=x*x;    double yy=y*y;    double zz=z*z;    double r=xx+yy+scale3*zz;    if(r>0)    {      Red+=xx/r;      Green+=yy/r;      Blue+=zz/r;    }    if (r>6)return false;    mr*=mrscale;    s1*=scale1m;    if (r<mr && i>maxi)    {      return true;    }    y=2*x*y+jy;    x=xx-yy+z1*zz+jx;    z=s1*z*Math.Pow(r,scale2)+jz;  }  return true;}public override void Init(){  base.Init();  if(GetString("intern.Formula.TempUpdateVal")!="df56cd74d98255c12094e43f12595f8c")  {    SetParameterBulk("Formula.Parameters: maxi=3 minr=0.0002 mrscale=1.13 scale1=1.61 scale1m=1.004 scale2=0.461 scale3=0.2 scalez=0.5 usecolors=0 z1=44 z4=0.99 Formula.Static: Cycles=555 Julia=0 jx=0.33 jy=0 jz=0 Scene: CenterX=0.340957877178389 CenterY=-0.0655349282756132 CenterZ=-0.000219581400425134 Radius=0.000361429050226264 Transformation.Camera: AngleX=-90 AngleY=0 AngleZ=0 IsometricProjection=0 Position=1 intern.Formula: TempUpdateVal=df56cd74d98255c12094e43f12595f8c");  }}

#### trafassel

• Fractal Friend
• Posts: 16

#### Re: Fake 3D Mandelbrot Set

« Reply #4 on: September 02, 2018, 05:39:05 PM »
Code: [Select]
public double minr;public int maxi;public double scale1;public double scale2;public double scale3;public bool usecolors;public double mrscale;public double scale1m;public double z1;double jx,jy,jz;public double scalez;public double z4;public override bool GetBool(double x,double y,double z){  if(z>0)  z=Math.Pow(z,z4);  z*=scalez;  jx=x;  jy=y;  jz=z;  x=_jx;  y=_jy;  z=_jz;  double mr=minr;  double s1=scale1;  double z3=scalez;  for (int i=1;i<_cycles;  i++)  {    z3*=z4;    double xx=x*x;    double yy=y*y;    double zz=z*z;    double r=xx+yy+scale3*zz;    if(r>0)    {      Red+=xx/r;      Green+=yy/r;      Blue+=zz/r;    }    if (r>6)return false;    mr*=mrscale;    s1*=scale1m;    if (r<mr && i>maxi)    {      return true;    }    y=2*x*y+jy;    x=xx-yy+z1*zz+jx;    z=s1*z*Math.Pow(r,scale2)+jz;  }  return true;}public override void Init(){  base.Init();  if(GetString("intern.Formula.TempUpdateVal")!="5a4283c35e74937b66cd6d965fd0eebf")  {    SetParameterBulk("Formula.Parameters: maxi=153 minr=0.17 mrscale=1 scale1=1.61 scale1m=1.004 scale2=0.461 scale3=0.2 scalez=0.1 usecolors=0 z1=21 z4=0.99 Formula.Static: Cycles=555 Julia=0 jx=0 jy=0 jz=0 Scene: CenterX=-0.703712616888288 CenterY=-0.34861488460146 CenterZ=-0.0110999789388717 Radius=0.00601311740030147 Transformation.Camera: AngleX=-71.7061323840061 AngleY=8.89341587538425 AngleZ=-15.8132056705929 IsometricProjection=0 Position=1 intern.Formula: TempUpdateVal=5a4283c35e74937b66cd6d965fd0eebf");  }}

#### quaz0r

• Fractal Friar
• Posts: 106

#### Re: Fake 3D Mandelbrot Set

« Reply #5 on: September 03, 2018, 11:06:23 AM »
nice! i really like some of these that seem to have a bit more going on than the usual whipped cream stuff

#### trafassel

• Fractal Friend
• Posts: 16

#### Re: Fake 3D Mandelbrot Set

« Reply #6 on: September 10, 2018, 01:38:28 AM »
Another way to fake the 3D mandelbrot: Design the shape of the mandelbrot by disturbing another 3D fractals. Here is use escape time algorithm for Kleinian group limit sets from JosLeys and Knighty. (http://www.fractalforums.com/index.php?topic=24728.0)

Code: [Select]
public double KleinR;public double KleinI;public double minBailout;public bool useLineOfSeparation;public double losXScale;public double losYScale;public bool classicFolding;// Escape time algorithm for Kleinian group limit sets from JosLeys and Knighty.// http://www.fractalforums.com/index.php?topic=24728.0public 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 >= KleinR*(0.52+losYScale*Math.Sin(losXScaleFactor*x)) )      {        x = KleinI-x;        y = KleinR-y;        z = -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;}
Parameters:
Code: [Select]
public override void Init(){  base.Init();  if(GetString("intern.Formula.TempUpdateVal")!="0256d0e4fc8d06ab3e756ce1ac354af8")  {    SetParameterBulk("Formula.Parameters: classicFolding=1 KleinI=0.009828904647462 KleinR=1.95409610447188 losXScale=0.6 losYScale=-0.22 minBailout=0.2 useLineOfSeparation=1 Formula.Static: Cycles=166 Julia=1 jx=0.019 jy=-0.034 jz=0 Scene: CenterX=6.08180264629283 CenterY=0.637672507930825 CenterZ=-3.21305014645458 Radius=0.000147989238364178 Transformation.Camera: AngleX=64.0933881879361 AngleY=-46.0090366814574 AngleZ=141.449287633522 IsometricProjection=0 Position=1 intern.Formula: TempUpdateVal=0256d0e4fc8d06ab3e756ce1ac354af8");  }}

#### gforce

• Fractal Friend
• Posts: 11

#### Re: Fake 3D Mandelbrot Set

« Reply #7 on: September 10, 2018, 03:15:46 AM »
Very cool, i guess that's what I have been trying to do for a while

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