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  MARVELLOUS images

The AbsBox with Scale=1.

Really nice and interesting renders, trafassel, very good stuff!

What about using abs(a+f)-f (for each axis a) and varying f values ?

also abs(a+f1)-abs(a-f2)-a with different f1 and f2 values.

DarkBeam, you are right. To work with the formula as julia set you have to replace

x=y=z=w=0; with  x=ar;y=ai;z=aj; (The position of the point to test).

The sphere inversion:
double mult=1;
if (length < 1e-5) {
 //     mult=Math.Sqrt(fixedRadius)/(minRadius);
 }   else
 if (length < fixedRadius) {
   mult=Math.Sqrt(fixedRadius)/(length);
 }

is the same as:
mult=1;
  if (r < fixedRadius && r>0) {
    mult=1.0/r;
  }
if minRadius is very small. In my tests both variants generates nearly the same pictures.

The pictures of the scale=1 AbsBox are generated with a very small bailout value. So in Reply #18  I have replaced:
double gr=50000; // bailoutValue
with
double gr=32; // bailoutValue

Here ist formula, I used for generation the julia movie. The get it to work in Gestaltlupe you have to press render two times. First to set the parameters. Second to render the picture. Hope, this will help you with the formula.


public override void Init() {base.Init();
if(GetString("intern.Formula.TempUpdateVal")!="33b6843e3102477181c51c97eaf7b578"){
SetParameterBulk(@"<Entry Key='Border.Max.x' Value='0.832922740362181' /><Entry Key='Border.Max.y' Value='1.590864959092' />
<Entry Key='Border.Max.z' Value='-0.01610155004377' /><Entry Key='Border.Min.x' Value='-3.20862914697999' />
<Entry Key='Border.Min.y' Value='-2.45068692825015' /><Entry Key='Border.Min.z' Value='-2.28947448667369' />
<Entry Key='Border.Min.zz' Value='0' />
<Entry Key='Formula.Static.Cycles' Value='120' /><Entry Key='Formula.Static.Formula' Value='-2' />
<Entry Key='Formula.Static.jx' Value='0.01' /><Entry Key='Formula.Static.jy' Value='0.08' /><Entry Key='Formula.Static.jz' Value='-0.01' />
<Entry Key='Formula.Static.jzz' Value='0' /><Entry Key='Formula.Static.MinCycle' Value='51' />
<Entry Key='Transformation.Camera.AngleZ' Value='12' /><Entry Key='Transformation.Perspective.Cameraposition' Value='0.3' />
<Entry Key='Transformation.Stereo.Angle' Value='-9' /><Entry Key='Transformation.Stereo.EyeDistance' Value='0.5' />
<Entry Key='View.Height' Value='720' /><Entry Key='View.Perspective' Value='1' /><Entry Key='View.Width' Value='1280' />
<Entry Key='intern.Formula.TempUpdateVal' Value='33b6843e3102477181c51c97eaf7b578' />");}
additionalPointInfo=new AdditionalPointInfo();}


// Simplified Mandelbox
public override long InSet(double ar, double ai, double aj,  double br, double bi, double bj, double bk, long zkl, bool invers) {

  double gr=50000; // bailoutValue
  double xx, yy, zz; // temp var
  long tw; // boring
  int n;
  double x=ar,y=ai,z=aj;
  double r_n = 0;
  double mult=1;

  xx = x * x; yy = y * y; zz = z * z;
  tw = 0;
  double r = xx + yy + zz;

  double scale = 1.05;

  // Surface Coloring
  additionalPointInfo.red=0;
  additionalPointInfo.green=0;
  additionalPointInfo.blue=0;

  for (n = 1; n < zkl; n++) {

  // Original box fold is replaced by x=abs(x); y=abs(y); z=abs(z)
  // Inspired by the work of Kali.
   
  // Comment out to use the original (Tglad) Mandelbox formula.

  // if (x > 1) x = 2.0 - x; else
  if (x < -1) x = -2.0 - x;
             
  // if (y > 1)    y = 2.0 - y;  else
  if (y < -1) y = -2.0 - y;
             
  // if (z > 1)   z = 2.0 - z; else
  if (z < -1) z = -2.0 - z;
             
  //  ; fold sphere onto itself

  xx=x*x;yy=y*y;zz=z*z;
  r = xx + yy + zz;

  if(r!=0) {
    additionalPointInfo.red+=xx/r;
    additionalPointInfo.green+=yy/r;
    additionalPointInfo.blue+=zz/r;
  }
           
  // Bailout Condition
  if (r > gr) {  tw = n; break; }

  mult=1;
  if (r < fixedRadius && r>0) {
    mult=1.0/r;
  }
  mult*=scale;
  x*=mult;
  y*=mult;
  z*=mult;

  // In Julia Mode: the fixed Julia values
  // In Mandelbrot set mode: the room coordinates of the pixel to test
  x+=br;
  y+=bi;
  z+=bj;
 }

  // For inside rendering
  if (invers) {if (tw == 0) tw = 1; else tw = 0; }

  return (tw);
}

Another zoom into the AbsBox:

<a href="http://www.youtube.com/v/gOS6vUIihM8&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/gOS6vUIihM8&rel=1&fs=1&hd=1</a>

Nice, that you like it.

The Disco-strobe lights comes from randomly generated shadows.