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The Mandelbox, but seen from the Inside. This means a voxel is visible, if and only if its coordinate is no element of the Mandelbox set.

In the center there is also a box. Rendered with low iteration.

Looks like the well known Bulb Trees.

Captivating and groundbreaking pictures. What scale did you use, and how many iterations?

I feel like exploring never before seen ocean depths. The grainy black and white feels like low light photography.

That's amazing trafassel  :o  :worm:

I used a changing scale value. The original Data can be found at:
http://github.com/trafassel/Gestaltlupe/blob/master/settings/Public/Examples/Mandelbox/Plants.xml

This data also includes the following formula (ar=-1.2,ai=0.01 ,aj=0.8 are fixed parameters ):

/// <summary>
        /// Initialisierung
        /// </summary>
        public override void Init() {
            base.Init();

additionalPointInfo=new AdditionalPointInfo();
            // Hier kann z.B. pow oder gr aus den Einstellungen gelesen werden.
        }


// 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;
double xx, yy, zz;
          long tw;
          int n;
          double x=0,y=0,z=0;
          double r_n = 0;

          xx = x * x; yy = y * y; zz = z * z;
          tw = 0L;
          double r = Math.Sqrt(xx + yy + zz);
  double scale = ar;
additionalPointInfo.red=0;
additionalPointInfo.green=0;
additionalPointInfo.blue=0;

          for (n = 1; n < zkl; n++) {
if(scale<-1)
scale=scale-ai*(scale+1);

//              ; fold box onto itself 
              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
              double fixedRadius = 1;
              double minRadius = 0.00001;
      double length=   r = Math.Pow(x*x + y*y + z*z,aj);
 //  double length=   r = x*x + y*y + z*z;


            if (length > gr) {
//additionalPointInfo.red=x*x/r;
//additionalPointInfo.green=y*y/r;
//additionalPointInfo.blue=z*z/r;
              tw = n; break;
            }

   double mult=1;

    if (length < minRadius) {
      //  mult=Math.Sqrt(fixedRadius)/(minRadius);
    }   else
 if (length < fixedRadius) {
        mult=Math.Sqrt(fixedRadius)/(length);
  }
   mult*=scale;
   x*=mult;
   y*=mult;
   z*=mult;
   x+=br;
   y+=bi;
   z+=bj;
          }


          if (invers) {
            if (tw == 0)
              tw = 1;
            else
              tw = 0;
          }
          return (tw);

        }

The bulb on the top.

WOW! Really cool images Trafassel!!!

I'd be interested to know what it looks like if aj is 0.5 and ai is 0. Does it affect the shape of the turnips? :)

The Bulb is a hole in the Mandelbox - and in this hole there is a hidden death star.

The inside of the death star

Whaooo! I want to see a video! :)

A inside view of the Mandelbox with aj is 0.5 and ai is 0 (I choose ar=-1.8 ) .


But I cannot find the the turnips.

The inside of the inside of the death star.

And a zoom into the picture above: a turnip garden

djeeeee, a russian egg...
i know in the 42 inkarnation there is a white rabbit   :D

woops, I meant aj=1 as in normal sphere inversion, and ai as 0, do turnips grow in that simpler formula? and do they look different?

OK, here is one with ar=-1.2 ai=0 and aj=1.

Looks "bulby", but also very dusty.

Very interesting Mandelbrot-set-like shapes on the sides.

Wow, thanks for trying it out, maybe its less dusty for ar=-1.1.
Reminds be a bit of the quasi-fuchsian.

I got some interesting structures on ar=-1.5 ai=0 and aj=0.7.

Zoom into the last picture.

... but the egg is not empty.

Oh, no there is it again - the spine.

ar=-1.1
ai=0.013
aj=1

Zoom into the spine.

Incredible pictures trafassel. Could the inner Mandelbox be actually the holy grail?....

... but the most intersting pictures comes from the combination
ar=-1.1
ai=0
aj=1

Tglad, that are ecactly your suggested parameters!

(ar,ai,aj)=(-1.1;0,1)

center of the last one

Holy smokes!

I have to agree! :o

unbelievable!

These pictures are amazing.

MOAR MOAR!


erm, please?

@Jesse : I 'd like to be able to do that in M3D !!! PLEASE :):)

Pearl    curtain at scale=-1.1

holy ... wow  :o
The ambiance remind me the submarine cameras of deepwater horizon  :alien:

Smooth structure in scale=-1.2 Mandelbox.

Fractal structures at scale=-1.2.

I like the way 96a turns into a fizz of bubbles at the top
The segments on 56a look like they're made of honeycomb  :alien:

Ok, back to scale=-1.1

Let me introduce Fridolin.

The are some spores (or eggs) in the honeycomb.

You wrong, its a black rabbit.

That's wonderful Trafassel! You've taken 3D fractals further into the unknown! bravo!  :joy:

Holy mandelbrot beauty!!!  O0

Rain?

Other type of house.

Other type of bulb: closed

Other type of bulb: open

These pictures are incredible :-)

Can you please explain how they are generated and what makes it different to the regular mandelbox? From what I read, the solid parts here represent the non-solid parts of the mandelbox?

And also what does ol' Skytopia fella make of this? Surely this meets the 'Holy Grail' requirements, with it's 'spheres surrounding spheres' analog to the Mandelbrot's circles?

The only difference to the regular Mandelbox is that minRadius in sphere folding is set to 0.00001. The view is from the inside - and yes, this means, the solid parts represent the non-solid parts of the mandelbox. The same definition of "inside" is used in the Skytopia pages. Here the fractal seems to have a limy surface (Example: "Caramelized Hazelnut Swirl").

The rendering was done with Gestaltlupe. Binary (Version 0.9.2) is available at: http://github.com/trafassel/Gestaltlupe/tree/master//bin/

Most of the scenes used here can be found at: http://github.com/trafassel/Gestaltlupe/tree/master/settings/Public/Unsorted/

Some fragments of the inside and the outside in one scene.

a step closer

I found a bat sitting on the corner.

Ok, lets start a new flight.

Now the box is open.

Thats it, the inside.

i love it  :o

Slight rotation to get a map of the whole scene (top and right part is skipped because of symmetry).

There are some interesting, some boring and some dusty places to visit.

avoiding the dust.

looks like fractal wonderland;

and this looks like ... oh no. Its so cool.

...

not the tunnel

some trees

or animal trees?

no trees, something different

found near the root of the tree

Reply #52 is fantastic.. O0 and now I can imagine a negative/internal KIFS.
I am so spoiled!

I want to go in there NOW!!!! :)

Stunning T!

As I said higher in this thread, the inner box is the closest thing to the Holy MandelGrail I have seen, and this example is particularly striking (Reply #63)

INCREDIBLE !!! :D

now it's possible to have semi-transparent 3d fractals/animations using alpha compositing.

My first steps in the inverse -1.1-Mandelbox as diashow movie mix.

http://www.youtube.com/watch?v=9AoRklaHLzE

... some unsorted pics from my last trip.

pic2

pic3

Amazing stuff trafassel. This is surely much closer to what I originally envisaged for the real 3D Mandelbrot than we've ever seen before. We're seeing all kinds of designs, giant 3D connected networks, tunnels, arrays of tentacles, intricate satellites, foamy materials, shapes we've never imagined, and of course, the return of the spine also! (closer to what I thought the 3D spine should look like). I love the zoom near the end of your video too.

If I were to give the Mandelbulb rating of how close I thought it was to the holy grail, say, 5/10, I would give yours perhaps 7 or maybe 8/10. I still think there are subtle and not so subtle things which prevent it from being the holy grail which I'll try to elaborate on soon. In particular, there's a feeling that many of the shapes have a somewhat IFS feel to them (over-smooth or chopped up spherical surfaces etc.), and of course the overall shape is not what we might expect.

But not to take away from this awesome find which is probably going to be the most fun exploring out of anything we've seen so far in my opinion. I could've been fooled, especially with scenes like:

http://www.fractalforums.com/index.php?action=dlattach;topic=4141.0;attach=3272;image
http://www.fractalforums.com/index.php?action=dlattach;topic=4141.0;attach=3268;image
http://www.fractalforums.com/index.php?action=dlattach;topic=4141.0;attach=3241;image

The Pandora's box meme has never been more appropriate because we actually looked inside! Actually, looking inside on the 'default' Mandelbox without your adjustments doesn't look nearly as good for some reason (often sparse 3D arrays of chopped up spheres from what I've found, like a starfield), though I haven't looked very far/wide/deep as of yet.

Congrats. The Mandelbox has gone even further up in my estimation now :)

... and pic4

Thanks for the nice words, twinbee.

One very intersting, question is: Why is the inside view so different from the outside view? Incidentally, the last picture is a outside view picture.

Inside and outside view in one picture (inside - outside the box)

Same monster, different scaling factor.

Increase scaling to get monster skin.

The Bridge

Yikes! You're growing aliens here.

not growing, but here is an ancient alien wall painting.

Inside (bottom) - outside (top) pics with scaling  -1.1 ... -1.03

next Inside (bottom) - outside (top) pics with scaling  -1.1 ... -1.03

Title page of an old science fiction story book.

A fractal in a fractal in a fractal ....

Life found: a bacteria.

zoom in reply #89

The alien (we see the backside of its head) show me the stars.

Great series Trafassel, keep them coming.

Out of curiosity, do you have the parameters of pic4 in reply #79, it is an outside view, right?
Because i have the feeling that the formula i use gives different results...

Object area (min/max Coordinates):

x:   -1.9757726114385599      -1.9757638018607651
y:   -1.9953273068042268      -1.995306136977542
z:   -0.85179063580878345    -0.85176740404776863

The original parameters are at:
http://github.com/trafassel/Gestaltlupe/blob/master/settings/Public/Unsorted/Data462pic10275.tomo


There is a slight difference between Tglads Mandelbox formula, and the formula uses in this thread: there is no minimal radius defined. Perhaps this is the difference in your formula.

double minRadius = 0.00001;
if (length < minRadius) {
   //  mult=Math.Sqrt(fixedRadius)/(minRadius);
  }   else
if (length < fixedRadius) {
  mult=Math.Sqrt(fixedRadius)/(length);
}

Another outside view

Ok, i thought it would be a zoomed out view on the main corner of the box  :dink:

So you are using now the original formula without varying the scaling and without the power function,
only with minr set to nearly 0... that explains something.  :)

Watch out, the monsters.

Here is another one.

A well.

A fractal tower.

A more geometrical spider web.

A tunnel (with a red bubble at the end) again.

The border between the blue and the red bubble land.

Left bottom corner of the last picture.

Loving these pictures :-)

What's inside the tunnel?
A view inside the tunnel, looking out might be nice.

Love the way you get all these tunnels. Is that tunnel the same breadth throughout and therefore faking perspective, or does it do what the other side of the Mandelbulb spine (cave) does and fake perspective by getting smaller and smaller?

Anyway, yeah, love to travel through there as miner49er said.

Perhaps this all are not tunnels and ends in a red or blue bubble like reply #46 . I don't know. Here is an sideview (and cut) of the last tunnel.



 

Here is a view from outside the mandelbox. The tunnels are inside this rings and thus ends in a green square.

This rings seems to be all over the Mandelbox. This picture of a regular negative Mandelbox (http://www.fractalforums.com/index.php?action=gallery;sa=view;id=3776) is a good example. Another sort of ring - or rainbow - is displayed in http://www.fractalforums.com/index.php?action=gallery;sa=view;id=3682 .

So many incredible pictures trafassel, you really are like a lone explorer, finding these weird and wonderful things in what seems like a deep underwater survey. Imagine what some of it would look like ray traced in high detail from within the caves, and refractions through all the bubbles etc.
reply #104 has that honeycomb again, looks cool
I like the monster things with their monster skin, and the caterpiller on a peanut in #90 is super cool!

Yes, it ends on a green square.

This additional tunnel pictures gives an overview of the properies of this special place.

Zoom into the sidepath on the left.

Thats true, i feel like an lone explorer. But this world is to big to explore for one man and two computers.

A picture for all honeycomb fans:

If you zoom into the honeycomb, you find this:

Very geometric subtunnels, and a horizontal folding line in the center. Changing scale affects the position of this line

... and all other folding lines.

The blue world contains tunnel2

Disharmonic double attractors

same disharmonic double attractors, scale=-1.03

the last two pictures are regular outside views (this also).

pseudo.negative.mb0x
(http://fc08.deviantart.net/fs71/f/2010/284/2/b/neg_mb0x_1_by_bermarte-d30k068.png)

(http://fc06.deviantart.net/fs71/f/2010/284/d/e/neg_mb0x_2_by_bermarte-d30k0oz.png)

(http://fc03.deviantart.net/fs71/f/2010/284/6/4/neg_box__by_bermarte-d30k2b9.png)

thanx to Trafassel/Knighty/Subblue
(http://fc03.deviantart.net/fs70/f/2010/284/6/c/neg_mb0x_3_by_bermarte-d30k15o.png)

(http://fc05.deviantart.net/fs70/f/2010/284/2/2/neg_mb0x_4_by_bermarte-d30k1gj.png)

(http://fc08.deviantart.net/fs70/f/2010/284/9/7/negative_mandelbox_tryout_by_bermarte-d30k1vt.png)

(http://fc06.deviantart.net/fs70/f/2010/284/5/8/neg_mb0x_5_by_bermarte-d30k1nx.png)

(http://fc05.deviantart.net/fs71/f/2010/284/f/e/neg_mbox_by_bermarte-d30k2nq.jpg)

Awesome trip! Thank you for taking us with you.  ;D

Nice to know, that I am not alone anymore inside the box. Picture 3 and the last one are my favorite.

Again I have combined all holiday pictures from my last trip into a short movie.
 
http://www.youtube.com/watch?v=gPCMulqW7fQ

Some of the inner structures are also visible on the outside.

Awesome video trafassel!  O0
A few long clips and many short clips.... fractal editing! :)

The center of the twin attractors. Is it possible, that the key to the understanding of this fractal is founded outside the box?

And the corresponding "inside".

It looks like the inside of the positive Mandelbox (scale +1.01) has also some interesting areas.

... but this areas are harder to find, and looks less aesthetic than similiar forms in the negative mandelbox. Is it, because the negative sign adds left-right symmetry?

Back to the well known !-1.1minRad0Mandelbox

where the monsters have 4 toes.

Question:
How many monsters (finite or infinite)?

Will this poor monster find his brother?

... and please ... a good way to add a rotation of |1-r| to all axis?

A finite number of brothers?

Attractor with scale=-1.1 and scale =1.14.

Attractor with scale=-1.03

Outer view, but changing scale factor (from -1.3 to -1)

The surface structure reminds me of thic picture of a disco ball in the -1.1minRad0Mandelbox.

This is also an ouside picture: a tunnel. Scale =-1.03

A typical "Inside" tunnel.

A symmetric multi tunnel.

These are so interesting - any chance of a fly-through of the insidebox?

(Just to be sure: the space you would be flying through, and that the "camera" is in for all these images, is where the "normal" Mandelbox has solid walls--and not just some space that is inside the normal Mandelbox, right? I keep getting confused! In other words it's the complement of the Mandelbox?)

Can you just flip a sign in the formula, and use the software to make an animation in exactly the same way as for the "normal" Mandelbox? Or is it more complicated than that?

There's a nice video a couple of pages back.
Yes, its the compliment of the mandelbox, but I don't think you can just flip a sign, it is harder to draw the inside of a fractal because there's no threshold so you have to iterate to the maximum number of iterations for each point along the ray for each pixel. (I think). So I think it is slower to calculate.

An interesting thing about the inside of the mandelbox is we think it is nowhere dense... so the inside views actually have structure everywhere... if you take any empty bit of space and look in really high detail I think there will be little strings of bubbles or fractal trees filling the space.

Yes, an inside video needs a lot more rendering time than an outside video. Tglad gives a good explanation, why the additional time is needed.

The "nowhere dense" hypothesis is new to me. I think, I can define an area in the -1.1minScale0Mandelbox where each point in this set is element of the Mandelbox set. But let me think about this.

In a 4-dimensional Mandelbox the objects appears more sparse.

In a 4-dimensional Mandelbox you can combine different fractal shapes into one objects.

the last one is a total upgrade of Fridolin!
:)

Sparse 4-dimensional Mandelbox scene.

I'm sorry? 4 dimensional mandelbox? .. woah O0 a 3d slice of it, I've never seen it before.

The nowhere dense idea is because there are no attractors (unlike 0+0i on mandelbrot) and so it is more like a menger sponge that happens to be a thicker sponge towards the middle. There is no area of the mandelbox that doesn't have tiny holes or cracks in it.
So reversing the logic, there is no area of space in the compliment mandelbox that doesn't have structure in it. A completely untested idea :)

The funny shapes of concentric circles are actually 'detractors', points straying too close to the centre of them get thrown towards infinity.

In the 4-D Mandelbox I added another folding operation (symmetric to the other x,y,z-foldings).

The original idea was given in:
http://www.fractalforums.com/3d-fractal-generation/folding-boxes-in-higher-dimentions/
but in interpreded the "higher dimension folding" not in this strong sense.

(Formula in: http://github.com/trafassel/Gestaltlupe/blob/master/settings/Public/Unsorted/Data493pic10164.tomo)

Now the "nowhere dense idea" makes sense for me. Has anyone try to prove this?

Another open question: How many monsters?

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

Detractors as 3D Slide in a 4D Mandelbox.

The "nowhere dense idea" is discussed in http://www.fractalforums.com/3d-fractal-generation/the-mandelbox-is-tenuous/

By searching for the Quasi-Fuchsian fractal i found this, which remainds me of the seahorses in #r43.

http://www.youtube.com/watch?v=yY1-D13KICw

Perhaps the most interesting objects inside the Mandelbox are made of fake Indra's Pearls.

Pearls.

The black part as 2D slide is interesting.

Ben Racken: Die Augen

http://www.youtube.com/watch?v=jytvQv1bTn0

Top of the tower in the last video.

Zoom in #r153

More awesome pics Trafassel. Have you tried an inner view of the scale -1 minr 0 mandelbox?
I originally thought it would be just a solid cube, but it isn't. There is structure on the corners and edges, but I'm not sure if it is fractal or smooth:

On second thoughts I'm wrong, it probably is a partial solid, just that the bailout distance has to tend to infinity as the scale gets closer to -1.

You have to stop now Trafassel, it is so beautiful on the inside I wish I had more time, but some day I will get deep into Gestaltlupe!!!  O0

I don't want to stop. First, there are some questions to check (all have to do with some sorts of infinity).

In the meantime a video from my new project Spacekekse:

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

Yes, everything in this video  (except some iteration count changing from 170 to 1700) is a  inside view of a 4 dimensional minScale=0  negative Mandelbox.

Music is done by Korg DS 10 on a Nintendo DS.

Wow, I particularly like the 'foaming' section starting at 1:12.

That is the only part in the film, where q (the new component in the dim4) ist greater than 0.01 .  Hard to find such a place.

Infinity or not infinity, that is the question.

But its an nice infinity. This is picture of the box attractor. After reding  Reply #157 and  Reply #158 at the same time, I forget the the scale -1 minr 0 mandelbox. And today I found out, that this must be a very nice fractal.


This is scale = -1.005 ,

Zoom in Reply #163

Zoom in: Zoom in Reply #164

Outside and inside view

Sorry, its not the only part. From 1.44 to 1.55 there is the same area.

Zoom in Reply #165

Original Gestaltupe output.

Zoom in Reply #167

(Postprocessing with Paint.NET)

Zoom in Reply #168

Zoom in Reply #169

Zoom in Reply #170

The circles are floating points artefacts.

Zoom in Reply #171

Oh, this indicates, that I reached the end of the double precision.

Ok, then back to the -1.1minScale0Mandelbox

people, please consider making up a new thread for a new fly in !