Welcome to Fractal Forums

There are some great shots of the interior of the mandelbox (http://www.fractalforums.com/3d-fractal-generation/amazing-fractal/ (http://www.fractalforums.com/3d-fractal-generation/amazing-fractal/)) lately, so I thought to gather some here-

(http://www.fractalforums.com/gallery/1/640_14_02_10_2_40_34.jpeg)
(http://www.fractalforums.com/gallery/1/853_15_02_10_10_24_56.jpeg)
(http://www.fractalforums.com/gallery/1/853_07_02_10_9_52_18.jpeg)
(http://www.fractalforums.com/gallery/1/1127_14_02_10_7_44_48.jpeg)

These are amazing. They're like fractal architecture. I can see these being used for SF spaceships and for video games.

I would really love to see the plane "clenched" between the two pairs of teeth in that last pic. I wonder if it actually is (heaven forbid) smooth, and if not, what fractal structures it contains.

Really nice images :)
I'm already curious when we'll see buildings from that :D

Its not smooth  :) even with lower iterations. In the ani you can see how pieces are punched off.
21 to 25 iterations:

(http://www.fractalforums.com/gallery/1/1127_16_02_10_7_06_09.gif)


A magnification with clipping to see into the eggs:

(http://www.fractalforums.com/gallery/1/1127_16_02_10_10_23_48.jpeg)

I guess, to explore this, one will have to be even more creative than for the Mbulb....

Indeed! I have hard time finding some nice flight path  :(

I actually meant because the interior you cut open there seems even more interesting than the surrounding eggs...

However, that's something to be done a lot more with the Mbulb too: Cut it open. :) And not nessecarily with a plane.
Most interesting would be if you could somehow seperate the interior based on special details in order to be able to work like a surgeon... Maybe a bit a morbid comparison but the most interesting interior view in an animal body is sorted by its organs.

A 2D-set doesn't quite have something like that, but a 3D-set could easily show them... :) (Well, also just in the skin ofcourse... Or was there any try yet to find an equivalent of colouring the interior?

I understand what you mean. Sounds interesting. The images in this topic are really cool, and I can't wait to see more.

hmmm... thinking about it, the Buddhabulb would probably contain interrior details...

I don't have the anim version of UF, so instead here is a sequence showing a walk (or climb) through.
[sooty artefacts fixed on most pictures by increasing 'DE adjustment' from 1 to 10]

Starting in a corridor facing outwards
(http://www.fractalforums.com/gallery/1/853_18_02_10_6_13_05_0.jpeg)

Walking forwards
(http://www.fractalforums.com/gallery/1/853_20_02_10_3_15_39.jpeg)

Looking down into arch
(http://www.fractalforums.com/gallery/1/853_20_02_10_3_15_03.jpeg)

Climbing down and peering out
(http://www.fractalforums.com/gallery/1/853_18_02_10_6_13_05_3.jpeg)

Climbing through gap and into hall
(http://www.fractalforums.com/gallery/1/853_18_02_10_6_13_05_4.jpeg)

Looking left
(http://www.fractalforums.com/gallery/1/853_18_02_10_6_19_15_0.jpeg)

Looking straight ahead again
(http://www.fractalforums.com/gallery/1/853_18_02_10_6_13_05_4.jpeg)

Climbing into the cradle
(http://www.fractalforums.com/gallery/1/853_18_02_10_6_19_15_1.jpeg)

Climbing up to the top balcony
(http://www.fractalforums.com/gallery/1/853_18_02_10_6_19_15_2.jpeg)

Into the arch
(http://www.fractalforums.com/gallery/1/853_20_02_10_3_14_07.jpeg)

Crawl in and peer down
(http://www.fractalforums.com/gallery/1/853_20_02_10_3_13_22.jpeg)

Squeezing in and looking straight down
(http://www.fractalforums.com/gallery/1/853_18_02_10_6_21_00.jpeg)

Totally wicked!  O0

Great walkthrough Tglad, i am T-glad u found this box!

J

Cool sequence. If you send me the file, I could try to do the animation.

Nice shots :)
Looking forward to bib's animation of it :)

As to the spottiness, it's actually just luck really that the delta DE algorithms work at all on the Mandelbox, having said that I would suggest try increasing the bailout value - if you do so you may also need to reduce the solid threshold slightly and of course render times will increase, but hopefully the spotiness will go.

Thanks David, it seems higher bailouts make it a little worse. On average there are less sooty streaks if it is reduced from 10240 to 1024, but the colours change to lower in the spectrum, more greys and greens. I'm not sure why the bailout needs to be more than about 50... it is the square of the distance right... so on a 2d mandelbrot you could use 4? and about the same for the mandelbulb. How could a point out at radius 30 be inside the set?

Bib, a vid would be sweet :D, the sequence is here http://www.fractalforums.com/index.php?action=gallery;su=user;cat=131;u=853 (http://www.fractalforums.com/index.php?action=gallery;su=user;cat=131;u=853) in the description of each pic are the parameters.

I launched the calculation of the animation in 1600*1000 with 1400 frames at 28 fps based on the above sequence with one or two added keyframes to smooth transitions (without antialiasing and motion blur). Should be ready on Monday ;-)

The larger the bailout the more accurate the distance estimates are (all methods) this is because generally speaking they rely on the bailout iteration approximating the infinite attractor rather than it simply indicating "not inside".

Another reason that could explain the spotiness is the values you're using for the "Minimum step distance", "Minimum search distance" and "Delta distance" (or if you still have "Automatically calculate distances" enabled). Typically for the Mandelbox try disabling "Automatically calculate distances", setting "Minimum step distance" to 100* smaller than the solid threshold, "Minimum search distance" 10* smaller still and "Delta distance" 10* smaller still (or even smaller to an absolute minimum of between 1e-14 and 1e-16).

Thanks David. I tried out variations of these values but nothing made much difference, but then I tried changing a few other values and found that change in the 'DE adjustment' from 1 to 10 fixed the problem. No idea how it works but the soot is gone! Bib, this could fix sooty problems in your vid too.

The pattern at the end of the sequence looks quite 2d, but with some fog and a close up you can see it isn't a dead end. You can climb through the hole and drop down, where you'll come out back into the cradle again.
(http://www.fractalforums.com/gallery/1/853_19_02_10_5_50_20.jpeg)

In that case a better solution is to change "DE adjustment" back to 1 and increase the value of the solid threshold by up to a factor of 10.

A non-zero "DE adjustment" modifies the actual solid thresholds used based on the distance from the viewpoint of the "solid" on a point by point basis and the correct value to use is 1.0 -- using a value of 10 means that further from the viewpoint points are registered as "solid" at much higher distance estimates.

Another two shots of the Mandelbox. It was inside Mandelbox but in not dense area (located near top of box)
Scale = -2

(http://www.fractalforums.com/gallery/1/640_20_02_10_7_15_46.jpeg)
http://www.fractalforums.com/index.php?action=gallery;sa=view;id=1684

(http://www.fractalforums.com/gallery/1/640_20_02_10_7_16_35.jpeg)
http://www.fractalforums.com/index.php?action=gallery;sa=view;id=1685

(http://www.fractalforums.com/gallery/1/492_20_02_10_9_12_46.jpeg)
http://www.fractalforums.com/index.php?action=gallery;sa=view;id=1686

@bib, It looks like high rack warehouse stock :)
Interesting view

Another interesting view from the inside of a gallery:

(http://www.fractalforums.com/gallery/1/492_21_02_10_12_15_29.jpeg)
http://www.fractalforums.com/index.php?action=gallery;sa=view;id=1687

just wondering: How would the 2D-equivalent look in this case? (eg cut through the central plane where z=0)
They all are very nice :)

Like this:

Awesome !
This seems to be a single frame from "Monsters Inc." ?

I see what you mean ;)
(http://i183.photobucket.com/albums/x141/rewriter42/MonsterInc0.jpg)

I think it should be scene with doors :)

Yep, the door warehouse is what I was thinking of :)

Ah OK I see :) I thought the image I posted did fit well due to the similar perspective setup ;)

Here is another one (which is a zoom in the previous one):
(http://www.fractalforums.com/gallery/1/492_21_02_10_8_22_05.jpeg)
http://www.fractalforums.com/index.php?action=gallery;sa=view;id=1691

Is that the scale 2 mandelbox? It looks quite unusual, like weird crystals  ;D

Yes, scale 2. On the right side, the large road turning right is the corner of a very small cathedral arch deep inside the box.

"A better solution is to change "DE adjustment" back to 1 and increase the value of the solid threshold by up to a factor of 10."

I was using 1e-6, at 1e-5 the soot is still there, at 1e-4 there is about half as much soot but the detail it getting lost due to high threshold.
DE adjustment 10 remains the only way I've found to remove the soot, and visually doesn't show any side effects.

Love all the pictures above (and the vids too!). Faves include:
http://www.fractalforums.com/gallery/1/640_14_02_10_2_40_34.jpeg
http://www.fractalforums.com/gallery/1/853_18_02_10_6_13_05_4.jpeg
http://www.fractalforums.com/gallery/1/853_18_02_10_6_13_05_0.jpeg
http://www.fractalforums.com/images-showcase-(rate-my-fractal)/interior-shots-of-the-mandelbox/msg13203/#msg13203
http://www.fractalforums.com/images-showcase-(rate-my-fractal)/interior-shots-of-the-mandelbox/msg13252/#msg13252

Still stunned by this new creature. I've finally managed to pull myself away from updating my render engine to play with it :) The number of parameters also seems higher than the Mandelbulb - there's a lot more to meddle about with. For example, the scale tends to produce thinner/thicker 'frames'. And the bailout number seems strangely tied and related to the iteration count. Yep, unlike the Mandelbrot/bulb, a different bailout will produce different results.

Judging by the initial enquiry by msltoe, it would also seem we can use other arbitrary shapes such as icosahedrons in the formula too?

Also, it would seem that a 2D version of this is possible right? Has the basic Mandelbrot formula of z = z + c ever been used for other fractals in this way? It would seem than the z=z+c equation is more generic/versatile than anyone ever imagined.

"Volcanic Archipelagos"

(http://www.skytopia.com/project/fractal/mandelbox/volcanic-archipeligos.jpg)


Crystal Shard Complex:

(http://www.skytopia.com/project/fractal/mandelbox/CrystalShards.jpg)

Lower iterations produce really nice architectural type shapes:
(http://www.skytopia.com/project/fractal/mandelbox/low-iters.jpg)

Here's a giant version of the object with a lower bailout than usual (click here for full size (http://www.skytopia.com/project/fractal/mandelbox/tribox.jpg))
(http://www.skytopia.com/project/fractal/mandelbox/tribox-s.jpg)



Some others I made last night:

Archway 1:
(http://www.skytopia.com/project/fractal/mandelbox/archway1.jpg)

Archway 2:
(http://www.skytopia.com/project/fractal/mandelbox/archway2.jpg)

Mbox corner:
(http://www.skytopia.com/project/fractal/mandelbox/corner.jpg)

Mbox terrain:
(http://www.skytopia.com/project/fractal/mandelbox/mbox-terrain.jpg)

Foam:
(http://www.skytopia.com/project/fractal/mandelbox/soundproof-foam.jpg)

great ones :D

Wait, twinbee's versions of "too low" bailouts... Wouldn't a cubic  of bailout be more effective for this kind of fractal?
(With the spherical bailout one can produce nice cuts, though :))

Super wow! seriously cool  O0 are all those shapes from the same mandelbox with a lower bailout? Surely the crystal shards don't come from the mandelbox?
There are a lot of parameters in the UF mandelbox, but if you don't allow tearing space (discontinuities), and stick with a symmetrical cube instead of cuboid, then the the number drops down to minRadius, fixedRadius and scale, since the size of the box only matters relative to minRadius and fixedRadius anyway. Scale=2 seems critical in some way, in that scale > 2 causes separate boxes rather than a big box. FixedRadius 1 and minRadius 0.5 appears to make the largest arches possible that meet at a point, so they are special in that way, but other values might be critical in other ways.

Other arbitrary shapes like icosahedrons should be possible, but it looks like you can't get continuity and symmetry at the same time. You can either tear space, or the folding will not have the symmetry of the polyhedron. For example, folding of a tetrahedron depends on which order you reflect about the 4 faces, if you aren't tearing space.
The bailout needs to be higher than mandelbrot/bulb. Above say 1024 (and say 400 iterations) changing the bailout doesn't affect the shape. I think the difference is that the radius is doubled each frame instead of squared, so values don't fly off to infinity nearly as quickly. I still don't understand why the bailout needs to be more than about 150.

Awesome pics. Am I right in thinking the high bailout mandelbox exists as a subset of the points in the lower bailout pics?

I suppose for that, one would need to look at the Anti-buddha-amazing-brot to really know.

P.S. I get sick of these compound fractal names. I hereby dub it the "ABAB fractal".  :dink:

Holy MO0ses! 

Beautyful images Twinbee!

(And all others too)

Twinbee, your images are great! I'm glad to see that you tackled the Mandelbox ;-)

Here is another one I did yesterday:
(http://www.fractalforums.com/gallery/1/492_22_02_10_7_59_14.jpeg)
http://www.fractalforums.com/index.php?action=gallery;sa=view;id=1702

yet another nice find :D

Timeroot: I'd call it Amazing Antibuddhabox, rather... that'd be AABB then :)

Or what about AntiBuddhaBoxAwesomeness? (ABBA) xD

Mandelbox, scale = 3

(http://www.fractalforums.com/gallery/1/640_21_02_10_10_55_15.jpeg)
http://www.fractalforums.com/index.php?action=gallery;sa=view;id=1700
http://krzysztofmarczak.deviantart.com/art/Inside-Tglad-s-Cube-fractal-5-154966951

@twinbee, I can't see your images. All are blank :(

@bib: Very nice shot, soft background. Reminds me of a castle battlement.

@buddhi: OOhhhh, the Emerald City, beautiful.    ...a fractal Toto would be very funny, I think. :-)
I can see the images on twinbee's post fine...

Whoa, buddhi, you just turned the Matirx-data-flow-effect-stuff into 3D :D
It looks amazing!

Thanks all. Buddhi, pics should be available now - my server was acting up before I think.

Love the green glowy one above. Looking back, Jesse, your pic here (http://www.fractalforums.com/gallery/1/1127_16_02_10_10_23_48.jpeg) really looks like an amazing Egyptian/Aztec landscape (old animations "Ulysses" and "Mysterious Cities of Gold" spring to mind!). Tons of this stuff could be used for films of all kinds I reckon. And it would look *better* than what they do currently use.


The rest do, and even the 'crystal shards' is only a slight modification. I was trying to speed the original algorithm (http://www.fractalforums.com/3d-fractal-generation/amazing-fractal/) up by cancelling squareroots, and found it wasn't really possible. To cut a long story short, here are the changes below. Maybe it would be nice to somehow elegantly generalize this small modification into your formula.


(I used a bailout of 20 and around 7-8 iterations.)

Attached is a pic of the whole object.


Perhaps use the icosahedron for the 'invert' stage (where it checked the radius), rather than the folding (cube) stage?


Excellent question - I'm not sure yet.

Other ideas include kram1032's one where the bailout is defined by a cube instead of a sphere, or maybe saying: point.x/y/z = 3 - point.x/y/z (or more/less than 3 etc.)

Tglad, what made you think of this fractal? Are there elements in it from other fractal types, or is the technique pretty new?

The crystal cavern is *cool*  ;D

"Tglad, what made you think of this fractal?"
It came from looking at the whipped cream issue on the mandelbulb. Z^2 is a conformal transform, any tiny circle will remain a circle when transformed. The triplex mandelbulb Z^2 is not conformal, a sphere gets squashed and stretched by the transform. Almost all nice looking fractals are conformal, e.g. indra's pearls, appollian gasket, sierpinski triangle etc.
But in 3d you can't do Z^2, or anything like it which is conformal. This is proven (http://en.wikipedia.org/wiki/Liouville's_theorem_(conformal_mappings) (http://en.wikipedia.org/wiki/Liouville's_theorem_(conformal_mappings))).
It says that in 3 dimensions or higher, the only conformal transformations are translation, rotation by a fixed angle, scale and sphere-inverse-plus-reflection.
I wanted a fractal that covers itself just like the mandelbrot does. That is impossible to do with the above set. But if you allow the transform to also be anti-conformal then you also can allow reflections about any plane. This allows you to fold (or reflect) the space over itself. The box fold is an example, if you then scale by 2 afterwards then we have a mapping which keeps small vectors close to the origin, but large vectors fly off to infinity, this is just like the mandelbrot.
msltoe's fractals did just this http://www.fractalforums.com/3d-fractal-generation/sierpinski-like-fractals-using-an-iterative-function/ (http://www.fractalforums.com/3d-fractal-generation/sierpinski-like-fractals-using-an-iterative-function/) and look awesome. I tried to improve on this idea by preventing discontinuities (no jumps in the mapping) and making use of the sphere inversion as a way to add variety to the fairly dull box-fold-only fractal.

Here's some new pics.
Throne
(http://www.fractalforums.com/gallery/1/853_24_02_10_1_45_48.jpeg)

Mountain entrance
(http://www.fractalforums.com/gallery/1/853_24_02_10_1_44_07.jpeg)

The +C is used so the fractal changes with location. Unfortunately, even though this is true, It looks like the mandelbox (and any similar objects) is missing a very nice property of the mandelbrot. In a mandelbrot, wherever you are, you can always navigate to a different area by zooming in on a minibrot, this keeps the shapes all mixing up at all detail levels. In the mandelbox each area sticks with its shapes as you zoom in, for example zooming in on an archway creates shapes out of lots of archways, zooming in on the disconnected cubes in the corner creates shapes out of disconnected cubes. You can't get to the disconnected cubes from inside the archways area by zooming.
I think the reason is that the mandelbox changes shape if you scale it each iteration, so it can never have proper mini-boxes. It comes down to it not using a Z^2 type operation, so back to square 1  ;D

The mandelbulb should retain this nice property, at least partially if not fully. So, I guess the optimal 3d Mandelbrot-like fractal depends on which properties you choose to keep in 3d... its certainly fun searching  :D

whoa! The haziness gives the whole thing an amazing depth and the perspective is mindboggling in the second image :D

  Here's a series of Mandelbox Hybrids I came up with over the past couple days.  The Mandelbox formula is awesomely compatible with a couple old formulas of mine.  Sortof balloony...  and sorry about the color schemes... haven't gotten around to writing (or finding ones in the software) good color schemes yet.

Here's a weird hanging blob in a Julia of Type D (they exist as little blobs inside other blobs inside of other blobs if you hack away at it...):
(http://www.fractalforums.com/gallery/1/1170_23_02_10_8_24_42_2.jpeg)

  A couple of Type B hybrids (I think the 13th order ones are different fold (3 maybe) and scale):
8th order (z^8) front:
(http://www.fractalforums.com/gallery/1/1170_24_02_10_9_43_31_1.jpeg)
8th order rear (zoomed I think):
(http://www.fractalforums.com/gallery/1/1170_24_02_10_9_43_31_0.jpeg)
13th order side:
(http://www.fractalforums.com/gallery/1/1170_24_02_10_9_43_32_3.jpeg)
1th order front:
(http://www.fractalforums.com/gallery/1/1170_24_02_10_9_43_31_2.jpeg)

  A couple type D hybrids:
3rd order side:
(http://www.fractalforums.com/gallery/1/1170_24_02_10_9_53_46_0.jpeg)
3rd order rotated 45 degrees (a little bit holey because I didn't increase z-resolution):
(http://www.fractalforums.com/gallery/1/1170_24_02_10_10_05_37.jpeg)
3rd order top zoom in (maybe altered scale?):
(http://www.fractalforums.com/gallery/1/1170_24_02_10_9_53_46_1.jpeg)

  The type D seems to be best around z^3... above that it gets spiky (especially the even z^n's (z^4,z^6....), below it is a bit weird (unless you change scale, fixed=min radius, etc...).

  Here's the 3rd order rotated 45 degrees with Scale=1 instead of 2 and one more iteration:
  This color scheme was the one that showed the most detail... sorry about any radiation poisoning that is incurred by viewage....
(http://www.fractalforums.com/gallery/1/1170_25_02_10_1_35_45_0.jpeg)