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Scale=-1.03

Scale=-1.001
Iterations=37000

Scale=-1.001
Iterations=37000, again

A look behind the curtain.

http://orbittrap.ca/?p=1980 (http://orbittrap.ca/?p=1980)

(Infinite?) Mandelbox Spiral

http://www.youtube.com/watch?v=3vo5JzwNZ8k

In the scale 1.1 Mandelbox with the additional x=|x| condition, I found an attractor garden.

A path

Zoom in the last picture

Zoom in the last scene with low (170) and high (370) iterations.

The road to infinity.

And here is an owl, sitting inside the positive scale mandelbox (scale=1.04))

The area around the attractors in the Mandelbox with scale=1.04 and minScale=0 looks similar to the negative Mandelbox.

A fractal that contains every other fractal! :) This is what I call amazing!

Have you seen this very well done summary? http://www.miqel.com/fractals_math_patterns/mandelbox_3d_fractal.html

I am really speechless! The mbox is really an infinite universe, how many years it will take to explore it ...? :D

Now maybe you understand why your formulae do not get as much attention as you expect, there is already so much to explore just in the Mandelbox :o ;)

Not every fractal. One is still missing :-)

Two other spots in the scale 1.04 Mandelbox.

The monster and the net.

another world.

And again, there is so much to explore.

The house of my grandmother.

Is not here.

Which way to go?

But in the box, most of the ways ends at a wall.

Negative scaling variant of the AbsBox, described in:
http://www.fractalforums.com/new-theories-and-research/mandelbox-variant-21/

Very "bulby" surface details, but some new structures.

trafassel,

 Surprisingly, the following is nothing more than an inverted Mandelbox (your invention) with

 params: scale=1, fold @ 0.5, and minr = 0. seed = 0,-4,0. found by dainbramage.

It seems to look like a Riemann sphere fractal.

(http://nocache-nocookies.digitalgott.com/gallery/7/803_14_06_11_2_32_47.jpeg)

-mike

Beautiful image, msltoe.

What is fold @ 0.5?

Thanks. I didn't know at first from Jesse's parameters, but trying it out on my code, Fold:0.5 means "if (x>0.5) x=1-x", etc. instead of the usual if (x>1)...

Very interesting formula, but I cannot reproduce it. With scale=1 I just just got spheres with center at (0,0,0).   :-(

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

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.

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); }

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

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.

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

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

Vegetation

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 :help:

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

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
 

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

Some sketches

Central station and the opera.

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

http://www.youtube.com/watch?v=amPt2xL5mHw