minScale0NegMandelbox

[msltoe]

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

[trafassel]

Thank you very much, Mike for sharing your parameters.

In my experiences all scale=1 julia sets are very fragile, corresponding the max iteration value. I was able to create an fractal shape with scale=1, but if I increase imax, the shape moves into dusk.

[trafassel]

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); }

[msltoe]

trafassel: Glad you got it to work. It raises lots of questions, such as

1) Are there other parameters that produce similar results but requires less camera finesse.
2) Can we introduce spirals?
3) Can we get a higher density of bulbs (through higher symmetry polyhedra) to make Romanesco-like fractals?
4) Does this bulbous discovery (originally found by Theli-at on deviantArt) re-awaken the possibility of a holy grail or is this as good as it gets?

-mike

[trafassel]

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.

[trafassel]

Back to another world. Here I found the others and myself.

[trafassel]

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

[trafassel]

Vegetation

[Buddhi]

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

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)

Code:

for(int i=0; i < maxiter; i++)
{
if (z.x<-0.5) {z.x=-1-z.x;} else {if (z.x>0.5) {z.x=1-z.x;}}
if (z.y<-0.5) {z.y=-1-z.y;} else {if (z.y>0.5) {z.y=1-z.y;}}
if (z.z<-0.5) {z.z=-1-z.z;} else {if (z.z>0.5) {z.z=1-z.z;}}
r = z.x * z.x + z.y * z.y + z.z * z.z;
if (r > 1.0) {r = 1.0;}
r = 1.0/r;
z *= r;
z.x += 0;
z.y += 0.5;
z.z += -3.0;
r = z.Length();
if(r > 48) break;
}

Thank you in advance for

[KRAFTWERK]

It works:

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

And scale=1!!!

...

Those images looks sooo Holy Grail:ish!!!  Nice ones Trafassel!

[msltoe]

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
 

[trafassel]

Buddhi,

The difference between your formula and mine is the handling of the bailout value.

I test the bailout before sphere folding and I use r=z.x*z.x+z.y*z.y+z.z*z.z.

You has the additional line:

r = z.Length();
if(r > 48) break;

Which got the Square Root of r (so you exit the Main loop, if r>=48*48). The shape is very fragile at higher bailout value - it should be there, but very very dusty.

Hope this helps (Additional to the remarks of msltoe)

Per

[trafassel]

Some sketches

[trafassel]

Central station and the opera.

[trafassel]

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>