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Author Topic: Interior shots of the Mandelbox  (Read 9909 times)
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Tglad
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« Reply #30 on: February 21, 2010, 09:50:18 PM »

Is that the scale 2 mandelbox? It looks quite unusual, like weird crystals  grin
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bib
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« Reply #31 on: February 21, 2010, 09:57:51 PM »

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.
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Tglad
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« Reply #32 on: February 21, 2010, 10:32:35 PM »

"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.
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twinbee
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« Reply #33 on: February 22, 2010, 12:10:13 AM »

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 smiley 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"




Crystal Shard Complex:



Lower iterations produce really nice architectural type shapes:


Here's a giant version of the object with a lower bailout than usual (click here for full size)




Some others I made last night:

Archway 1:


Archway 2:


Mbox corner:


Mbox terrain:


Foam:


« Last Edit: February 22, 2010, 12:48:03 AM by twinbee » Logged
kram1032
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« Reply #34 on: February 22, 2010, 12:32:44 AM »

great ones cheesy

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 smiley)
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Tglad
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« Reply #35 on: February 22, 2010, 02:28:45 AM »

Super wow! seriously cool  afro 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?
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Timeroot
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« Reply #36 on: February 22, 2010, 02:52:05 AM »

Wouldn't a cubic  of bailout be more effective for this kind of fractal?
(With the spherical bailout one can produce nice cuts, though smiley)
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".  wink
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KRAFTWERK
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« Reply #37 on: February 22, 2010, 10:04:01 AM »

Holy MO0ses! 

Beautyful images Twinbee!

(And all others too)
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bib
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« Reply #38 on: February 22, 2010, 10:47:50 AM »

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/index.php?action=gallery;sa=view;id=1702
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kram1032
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« Reply #39 on: February 22, 2010, 03:13:18 PM »

yet another nice find cheesy

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

Or what about AntiBuddhaBoxAwesomeness? (ABBA) xD
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Buddhi
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« Reply #40 on: February 22, 2010, 05:37:07 PM »

Mandelbox, scale = 3


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 sad
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Timeroot
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« Reply #41 on: February 22, 2010, 09:07:49 PM »

@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...
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Someday, man will understand primary theory; how every aspect of our universe has come about. Then we will describe all of physics, build a complete understanding of genetic engineering, catalog all planets, and find intelligent life. And then we'll just puzzle over fractals for eternity.
kram1032
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« Reply #42 on: February 23, 2010, 02:35:44 PM »

Whoa, buddhi, you just turned the Matirx-data-flow-effect-stuff into 3D cheesy
It looks amazing!
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twinbee
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« Reply #43 on: February 23, 2010, 11:21:54 PM »

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 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.

Quote
Surely the crystal shards don't come from the mandelbox?

The rest do, and even the 'crystal shards' is only a slight modification. I was trying to speed the original algorithm 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.

Code:
 
Replaced:
float length = point.Magnitude()
...with...
float length = point.x+point.y+point.z  // Removes the square of each.

Replaced:
if (length < minRadius)
...with...
if (length < minRadius*minRadius)


Replaced:
elseif length < fixedRadius
...with...
elseif (length < fixedRadius*fixedRadius)

Replaced:
point.MultiplyEquals(sqr(fixedRadius)/sqr(length))
...with...
point.MultiplyEquals(sqr(fixedRadius)/length)

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

Attached is a pic of the whole object.

Quote
Other arbitrary shapes like icosahedrons should be possible

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

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

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?


* CrystalCavern-whole.jpg (141.26 KB, 800x800 - viewed 379 times.)
« Last Edit: February 23, 2010, 11:57:44 PM by twinbee » Logged
Tglad
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« Reply #44 on: February 24, 2010, 01:50:36 AM »

The crystal cavern is *cool*  grin

"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)).
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/ 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


Mountain entrance


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  grin

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  cheesy
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