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Trafassel,

 The main parameters are very unique so far, I can't seem to reproduce the shapes with alternate numbers.

  a=0;c=0.5;b=-3;
  while ((norm<48)&&(iter<imax)) {

   if (x<-0.5) {x=-1-x;} else {if (x>0.5) {x=1-x;}}
   if (y<-0.5) {y=-1-y;} else {if (y>0.5) {y=1-y;}}
   if (z<-0.5) {z=-1-z;} else {if (z>0.5) {z=1-z;}}

   r=x*x+y*y+z*z;
   if (r>1.0 ) {r = 1.0;}
   r = 1/r;
   x *= r;
   y *= r;
   z *= r;
    x = x+a; y = y+b; z = z+c;

   norm = x*x+y*y+z*z;
   
   iter++;
 }

view box:

    st[0].xstart = -0.5; st[0].xstop = +0.5;
    st[0].ystart = -3.1; st[0].ystop = -2.1; 
    st[0].zstart = -3; st[0].zstop = +1; 

rotate around x axis 45-90 degrees.
also, I put a cutting plane at z=0 after rotation.

-mike

It works:

Two scenes with norm=48 and norm=12  (in my Formula: bailout value gr).

And scale=1!!!

// Gestaltlupe 1.1 Formula with initialisation
// 1. Start Gestaltlupe
// 2. Select Tab Formula
// 3. Replace formula text with this whole text
// 4. Press Preview two times:
//      1. to set the parameters
//      2. to preview the rendering


public override void Init() {base.Init();
if(GetString("intern.Formula.TempUpdateVal")!="71bcef12b3fd03d2bde0dc7b1b98a86c"){
SetParameterBulk(@"<Entry
Key='Border.Max.x' Value='-2.6589457308563' /><Entry
Key='Border.Max.y' Value='3.45711283860699' /><Entry
Key='Border.Max.z' Value='0.564950190451428' /><Entry
Key='Border.Max.zz' Value='0' /><Entry
Key='Border.Min.x' Value='-3.36127769244752' /><Entry
Key='Border.Min.y' Value='2.75478087701577' /><Entry
Key='Border.Min.z' Value='-0.137381771139796' /><Entry
Key='Border.Min.zz' Value='0' /><Entry
Key='Formula.Static.Cycles' Value='2' /><Entry
Key='Formula.Static.Formula' Value='-2' /><Entry
Key='Formula.Static.jx' Value='0.01' /><Entry
Key='Formula.Static.jy' Value='0.0' /><Entry
Key='Formula.Static.jz' Value='0' /><Entry
Key='Formula.Static.jzz' Value='0' /><Entry
Key='Formula.Static.MinCycle' Value='200' /><Entry
Key='Transformation.Camera.AngleX' Value='10' /><Entry
Key='Transformation.Camera.AngleY' Value='0' /><Entry
Key='Transformation.Camera.AngleZ' Value='20' /><Entry
Key='Transformation.Perspective.Cameraposition' Value='0.5' /><Entry
Key='View.Height' Value='1200' /><Entry
Key='View.Perspective' Value='1' /><Entry
Key='View.Width' Value='1200' /><Entry
Key='intern.Formula.TempUpdateVal' Value='71bcef12b3fd03d2bde0dc7b1b98a86c' />
");
}additionalPointInfo=new AdditionalPointInfo();}

public override long InSet(double ar, double ai, double aj, double br, double bi,
double bj, double bk, long zkl, bool invers) { double gr=48; double xx, yy, zz;
long tw; int n; double x=ar,y=ai,z=aj; double r_n = 0; xx = x * x; yy = y * y;
zz = z * z; tw = 0L; double r = Math.Sqrt(xx + yy + zz); double scale = 1.0;
additionalPointInfo.red=0; additionalPointInfo.green=0; additionalPointInfo.blue=0;
for (n = 1; n < zkl; n++) {
if (x > 0.5) x = 1.0 - x; else if (x < -0.5) x = -1.0 - x; if (y > 0.5) y = 1.0 - y;
else if (y < -0.5) y = -1.0 - y; if (z > 0.5) z = 1.0 - z; else if (z < -0.5) z = -1.0 - z;
xx=x*x;yy=y*y;zz=z*z; double length= r = xx + yy + zz; if(r!=0) { additionalPointInfo.red+=xx/r;
additionalPointInfo.green+=yy/r; additionalPointInfo.blue+=zz/r; } if (length > gr) {
tw = n; break; } double mult=1; if (length < 1 && length>0)
{ mult=1.0/(length); } mult*=scale; x*=mult; y*=mult; z*=mult;/* x+=br;
y+=bi; z+=bj;*/ x+=0; y+=0.5; z+=-3; }if (invers) {if (tw == 0) tw = 1; else tw = 0; }
return (tw); }

Mike,
I think, some of your questions are connected with the shape of the "ideal" Mandelbox with very high bailout, very hight number of iterations and scale = 1. The best we can do first, is to find a good shape approximation (I think, scale=1.001 is another type of approximation) which need less computing time.

Here is a Julia of your formula with seed (0,0,-3.14) and a cut plane at y=0.

The more pictures of the Mandelbox, which is introduced in Reply #20 .

I'm trying to reproduce this formula (in Mandelbulber program) but unfortunatelly it not working for me 
Bellow there is code which I used. Please look what is wrong with it. I tried with many different intersections, but always got nothing. Maybe something is missed.

z is the iterated vector (z.x, z.y, z.z)

Thank you in advance for

Buddhi,

  The density has to be inverted. If the function escapes , it is solid and vice-versa.
  The number of iterations should be fairly high : 30-50.
  Finally, the structures are hiding inside the solid, near y=0.

-mike
 

Some sketches

A video of the Reply #20 Mandelbox variant. It shows the honeycomb area.

<a href="http://www.youtube.com/v/amPt2xL5mHw&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/amPt2xL5mHw&rel=1&fs=1&hd=1</a>