My fractal in a box

October 7, 2010 10:26 AM

Take a trip through the Mandelbox. (You may wish to hit mute and provide your own sound.) Make your own with Mandelbulber.

Much more from xlace.

posted by Burhanistan (34 comments total)

And, this one by the same person.
posted by Burhanistan at 10:34 AM on October 7, 2010

These 3-dimensional fractal objects leave me feeling to uneasy when I look at them, it's difficult for me to watch this. I don't know why I have this reaction -- they should be simply beautiful. Instead, to me, they look like something which Giger would create while residing in Pinhead's hell as set design for a Cthulhu movie.
posted by hippybear at 10:40 AM on October 7, 2010

Cool - but this would be much cooler if it was how I originally read it:

Mandrellbox
posted by MCMikeNamara at 10:43 AM on October 7, 2010

*groan*
posted by Burhanistan at 10:45 AM on October 7, 2010

So glad I clicked that. I see the word fractal and kinda think, yeah been there done that. But these are a joy. Lacy flying buttress Escher churches organically grown.
posted by Babblesort at 10:49 AM on October 7, 2010

Vague suspicions that the CIA's been dumping their surplus LSD in the water supply again. But if the result is this good looking, why the heck not?

also, when the singularity comes, I want my spaceship to look like that hybrid fractal one
posted by Ahab at 10:51 AM on October 7, 2010

it's difficult for me to watch this.

I get the same reaction. I think it's because it's an apparently architectural or sculptural object that has absolutely nothing to do with us.
posted by theodolite at 10:53 AM on October 7, 2010 [1 favorite]

absolutely nothing to do with us

I think those are technically known as 'eldritch geometries' by architects.
posted by everichon at 10:56 AM on October 7, 2010 [4 favorites]

I tend to prefer a little more Cyclopean and a little less non-Euclidean.

Ia! Ia!
posted by WinnipegDragon at 10:58 AM on October 7, 2010 [1 favorite]

This is how the Borg cube should've been designed.

TWPLs_out_of_place_Star_Trek_reference_postcount++
posted by The Winsome Parker Lewis at 11:01 AM on October 7, 2010 [2 favorites]

Fractals viewed at a set scale are cool and all, but they only really get the psychedelic juices flowing when you zoom in on new detail.
posted by vectr at 11:22 AM on October 7, 2010

"Pathological monsters!" cried the terrified mathematician,
"Every one of them is a splinter in my eye."
posted by cerebus19 at 11:24 AM on October 7, 2010

This animated Sierpinski triangle is pretty awesome, apparently done by manipulating various parameters set to music. It has this crazy pulsating effect that looks very... liquidy I guess.
posted by delmoi at 11:45 AM on October 7, 2010 [1 favorite]

I think much of the unpleasantness described comes from their color choice, which is kind of grimy-gory. Remember, fractals don't have "color," only color-keyed interpretation of some aspect of the math. In the case of the Mandelbrot set, this is how quickly the point diverges to infinity. But the actual colors used are an aesthetic choice on behalf of the renderer. (Or maybe in this case, the lack-of-aesthetic choice.)
posted by JHarris at 12:31 PM on October 7, 2010

Are these procedurally generated? It seems like they must be, but then you get those weird instances where the renderer seems to cheat and just makes things blurry, as if they were outside of the depth of field.
posted by invitapriore at 1:17 PM on October 7, 2010

I think those are technically known as 'eldritch geometries' by architects.

These are soooooo close to getting the angles just right. Patience, patience...
posted by FatherDagon at 1:18 PM on October 7, 2010 [1 favorite]

The first video starts off uncomfortably grotesque, like a fungus or the inside of a Flood-infested megastructure. But about 3/4ths of the way through it morphs into an overgrown Mayan space-sewer. And the second one is even better -- it reminds me a lot of the beginning of the Second Renaissance anime from The Animatrix. I just wish I had a computer powerful enough to render stuff like that.
posted by Rhaomi at 1:40 PM on October 7, 2010

Metafilter 4chan: an overgrown Mayan space-sewer
posted by everichon at 2:00 PM on October 7, 2010

Mandelbox

The Borg have kicked it up a notch in cube design.
posted by aught at 2:02 PM on October 7, 2010

I just had a moment of cultural fugue where I conflated the Borg with the Cenobites from Hellraiser. But, like the time you got your chocolate into my peanut butter, IT KIND OF WORKS.
posted by everichon at 2:08 PM on October 7, 2010

> IT KIND OF WORKS

You must assimilate...to the pain.
posted by Burhanistan at 2:10 PM on October 7, 2010

These are pretty, but I don't like that they are named after Mandelbrot, as if complicated trippy shapes were all that was involved with the Mandelbrot set. As vectr points out, there is no zooming here, you are just wandering in an ornate palace. When you zoom into a fractal, more and more detail is resolved, from shapes that you could already see. The only reveals here are going around corners. I don't know how this Mandelbulber program works, but it doesn't appear to use self-similarity at infinite scales, which is pretty much the definition of a fractal.

It should be called Mandalbulber instead of Mandelbulber, because it has more in common with mandalas than Mandelbrot sets.
posted by bitslayer at 2:29 PM on October 7, 2010

bitslayer: "These are pretty, but I don't like that they are named after Mandelbrot, as if complicated trippy shapes were all that was involved with the Mandelbrot set. As vectr points out, there is no zooming here, you are just wandering in an ornate palace. When you zoom into a fractal, more and more detail is resolved, from shapes that you could already see. The only reveals here are going around corners. I don't know how this Mandelbulber program works, but it doesn't appear to use self-similarity at infinite scales, which is pretty much the definition of a fractal.

It should be called Mandalbulber instead of Mandelbulber, because it has more in common with mandalas than Mandelbrot sets"

It seems from the various descriptions I've seen that Mandelboxes are indeed self-similar at infinite scales. The detail is on the surfaces, you can zoom into them infinitely and find new stuff, as I understand it.

It's just that the macro structure of the Mandelbox is also very interesting and pretty, so people tend to also animate a lot of fly-throughs without that much zooming. But for instance this is much more of a zoom, and seems to show a lot of detail for at least a reasonable zoom level.

I think the problem with Mandelbox zooms is also computing capacity, since complexity increases with zooming much faster than in a 2D fractal.
posted by Joakim Ziegler at 2:48 PM on October 7, 2010 [1 favorite]

Yes, that one does have several levels of zoom. I like that better than the original links. But I still wonder if the computing capacity problem might arise because they are not literally self similar, so the entire structure needs to be stored in memory or something. The Mandelbrot set, after all, can be derived from a very simple equation.
posted by bitslayer at 3:12 PM on October 7, 2010

It's like an exploratory mission into some long-abandoned alien mega city. All white stone and creeping vegetation, levitating islands and everted cathedrals.
posted by lucidium at 3:47 PM on October 7, 2010

Hey Cortex. Something else to build on the Minecraft MP server.
posted by Splunge at 3:56 PM on October 7, 2010

But I still wonder if the computing capacity problem might arise because they are not literally self similar, so the entire structure needs to be stored in memory or something. The Mandelbrot set, after all, can be derived from a very simple equation.

The Mandelbox has a simple equation (although not as simple as the Mandelbrot's) and it is based on the same basic principle: repeatedly apply a formula to a point (either on the complex plane, or in 3D space) and if it ends up spiraling off to infinity, it's not in the set, otherwise it is.

The self-similarity comes from the "folding space onto itself" at each iteration, which means that 1 or more areas of the 2D plane/3D+ space (before the formula is applied) will map to the same area after the formula is applied, and will therefore resemble each other. Think of it like pointing a TV camera at two or more TV sets showing a live feed of what the camera is capturing (or more precisely, captured on the previous frame). Since the result of one iteration of the formula feeds into the next iteration, there is a feedback loop going on producing copies at smaller and smaller (or larger and larger) scales, with the number of copies doubling (or tripling, quadrupling etc) each time.
posted by L.P. Hatecraft at 6:54 PM on October 7, 2010 [1 favorite]

These things scare me. I just know, if in some future day I own a computer capable of rendering Mandelboxes in realtime, I will dive in and never, ever come out.

Here's a Mandelbox zoom (and another) that shows some of the mind-blowing fractal nature of these things.

And here's a site dedicated to insanely high quality fractal animations (2GB for a 30 second animation).
posted by straight at 8:30 PM on October 7, 2010 [1 favorite]

Okay, this is the best 3D fractal zoom I've seen.
posted by straight at 8:52 PM on October 7, 2010

This was amazing! A religious experience. I didn't experience any revulsion or unpleasantness, and I'm kind of disappointed to hear that so many others did. I would like to watch this in a theater. For a half hour. With 3-D glasses. At Alamo Draft House. Beer in hand. Before my movie starts. Don't know why I'm typing. In sentence fragments.

These are pretty, but I don't like that they are named after Mandelbrot, as if complicated trippy shapes were all that was involved with the Mandelbrot set.

No. The aptly-named Mandelbulb is the same equation as the Mandelbrot set, but with 3-D hypercomplex numbers used instead of 2-D complex numbers. It is a direct extension of the Mandelbrot set into three dimensions. The Mandelbox is just some further mental gymnastics around the same basic geometric idea (fold/twist/stretch somehow, add the starting vector, iterate).

The only reveals here are going around corners. I don't know how this Mandelbulber program works, but it doesn't appear to use self-similarity at infinite scales, which is pretty much the definition of a fractal.

Fractals don't use self-similarity so much as produce it. You iterate a certain equation and beauty and self-similarity just happen on their own. These fractals are also highly self-similar, as you can see if you watch closely. No, this doesn't do zooming, and that's fine with me. It's gorgeous as-is.

absolutely nothing to do with us

I don't agree. Much of art consists of creating patterns that appear beautiful to us. All patterns can be described by some mathematical structure. What an artist or sculptor does is find a specific pattern (mathematical structure) that is appealing. That is exactly what the math guys who found these patterns did. They tried many, many things, and kept the patterns that were beautiful.
posted by Xezlec at 10:34 PM on October 7, 2010

This is neat: Mandelbox Variations— looks like a picture of a mandelbox as some of its parameters are continuously varied.

Also, did anyone else see the CREEPY MANDELSKULL at around 1:50 in the first-linked video?
posted by hattifattener at 1:19 AM on October 8, 2010

everichon: "absolutely nothing to do with us

I think those are technically known as 'eldritch geometries' by architects"

What causes that feeling for me is that there is no sense of scale there (and, in a true fractal, would in fact not really be possible). I used to paint miniatures, and one thing I learned quickly is that you have to exaggerate the highlights and shadows on them to make them look "real". In this perfectly lit computer-rendered world the light does not behave like it would in reality, going up and down the scale - this seems to cause much of the confusion, because your brain will look for clues from the lighting (a huge object will never cast as clearly delineated a shadow as a small one, diffraction effects show up if the objects become very small etc.) that are just not present.
posted by PontifexPrimus at 6:21 AM on October 8, 2010

This is neat: Mandelbox Variations— looks like a picture of a mandelbox as some of its parameters are continuously varied.

These morphing ones look like they're being rotated through a higher dimension.
posted by straight at 9:01 AM on October 8, 2010

straight: "These morphing ones look like they're being rotated through a higher dimension"

They look like a mutant cauliflower that's come to devour us.
posted by Joakim Ziegler at 2:57 PM on October 19, 2010