Infinite diversity in infinite combinations

March 25, 2011 8:20 AM

Since they were first discovered just a few years ago Mandelbulbs (a remapping of the 2D Mandelbrot set into 3D space) have grown in diversity, becoming more exotic, ornate, and animated. They’ve even inspired their own fanbase and usergroups.

Some Mandelbulb explorations have the feel of epic science fiction - appropriate, since Mandelbulbs were first proposed by SF writer and mathematician Rudy Rucker 20 years ago, Visually, the work of Rena Jones and Jock Cooper also deserve notice, even if they use hybrid fractals, much like the Menger Sphere Sponge by Tom Beddard. More traditional artists using Mandelbulbs (sometimes referred to as “fractalists”) include Tom Wilcox and James Knowles.

If you’d like to start making your own Mandelbulbs, there are a variety of tools. Tom Beddard has the (previously mentioned) browser-driven FractalLab, as well as a Mandelbulb Ray Tracer (and a fun Escher Droste Effect filter) for PhotoShop’s Pixel Bender plugin. There’s also Fragmentarium and the related StructureSynth, along with Mandelbulb3D, Mandelbulber, XenoDream and Visions of Chaos.

“Deep zooms” of traditional Mandelbrot sets give you an idea where all this diversity comes from. While not exactly fractal, I thought Taras Hrabowsky’s ThingPit was also worth watching, if you like collapse-of-the-universe animation. Mandelbulbs previously on the blue, along with StructureSynth and Benoit Mandelbrot.

posted by Bora Horza Gobuchul (35 comments total)

Nice well researched post. The only suggestion I would make is put as less material as possible on the front page, and put the bulk of the post inside the thread.
posted by wheelieman at 8:24 AM on March 25, 2011 [1 favorite]

Mandelbulb! Mandelbulb!
posted by dirigibleman at 8:33 AM on March 25, 2011 [4 favorites]

Thoughts while watching first link:

"Oh hey cool, it's a fractal! Heh, that kind of looks like a piece of cauliflower. Oh weird, I think I just saw an atomic explosion...wait...morphing into a human brain? Is this thing trying to communicate with me? I think I need to go lay down."
posted by Demogorgon at 8:34 AM on March 25, 2011 [2 favorites]

Wow. Remember when stuff like this was the trippiest shit on the block?
posted by The Card Cheat at 8:38 AM on March 25, 2011

[Threw a bunch more inside, that was a lot of space on the front page. Carry on!]
posted by cortex at 8:38 AM on March 25, 2011 [2 favorites]

I got your 3d fractal right here.
posted by anigbrowl at 8:40 AM on March 25, 2011 [1 favorite]

Wow, the HD version on the first link is awesome. Would pay $20 for IMAX.
posted by a robot made out of meat at 8:42 AM on March 25, 2011

Oh my god, it's full of holes! These are really cool. I thought that the creepy music made them, well, kind of creepy.
posted by carter at 8:47 AM on March 25, 2011

Wow, the HD version on the first link is awesome. Would pay $20 for IMAX.

Here's something that might approach that.

If you ever get a chance, see Enter The Void in theaters (or on the biggest screen you can find). It was the most breathtaking visual adventure I've ever experienced.
posted by fantodstic at 8:47 AM on March 25, 2011

Wow, the HD version on the first link is awesome.

It's pretty much what I have always imagined science-fictional out-of-control nanotech would look like as it devours the world. Which is to say, scary.
posted by aught at 8:47 AM on March 25, 2011 [1 favorite]

I love this post. Thanks for this!
posted by fantodstic at 8:48 AM on March 25, 2011

This is all awesome, but that ThingPit link broke my brain.
posted by 40 Watt at 8:48 AM on March 25, 2011

I dunno whether someone spiked my juice box, or the drugs aren't working as they should, but jeez I'm glad it's happening..
posted by Ahab at 8:49 AM on March 25, 2011

Relatedly, 4-dimensional fractals projected into 3-dimensional space.

Ïa! Ïa!
posted by logicpunk at 8:52 AM on March 25, 2011 [2 favorites]

ThingPit is actually the trailer for the new Roland Emmerich disaster epic You'll Watch Anything with 'Splosions.
posted by Mister_A at 8:56 AM on March 25, 2011

Previously.
posted by Burhanistan at 9:07 AM on March 25, 2011

I know lots of people find these interesting and beautiful, but they give me the heebie-jeebies like close-ups of bugs do. (no offense to any entomologists among us!)
posted by LN at 9:14 AM on March 25, 2011 [1 favorite]

I'm with you, LN. After seeing a bunch of hi-res rendered stills of mandelbulbs and knowing how completely squidgy looking at those made me feel, I'm a bit hesitant to even click on these videos.
posted by hippybear at 9:19 AM on March 25, 2011

Can someone explain to me what exactly is going on when the Mandelbulbs appear to be morphing? Are they not actually (theoretical) solid objects? Are they being rotated through another dimension or something?

Mandelbrot-style fractals don't change shape like that, they have a set shape that you can examine at (theoretically) any level of detail.
posted by straight at 9:20 AM on March 25, 2011

Think that morphing one is a 4D julia set being rotated through one of the dimensions.
posted by joegester at 9:33 AM on March 25, 2011

Oh god, I wish I were high right now. No, wait, then I'd be terrified.
posted by notsnot at 9:37 AM on March 25, 2011 [1 favorite]

Obligatory "Metafilter's own" Jock Cooper inserted here.
posted by PapaLobo at 9:38 AM on March 25, 2011

I havn't seen the new TRON movie yet, since I heard it sucks. But I was thinking, they should have just made it a bunch of fractal stuff for like 90% of the movie. That would have been awesome.

Also, if you can do cross-eye 3D this is pretty awesome.
posted by delmoi at 10:01 AM on March 25, 2011

If DMT is the cinema, mandlebulbs are the Oscar nominees.
posted by not_that_epiphanius at 10:04 AM on March 25, 2011

I keep expecting to see a WE BRAKE FOR NOBODY bumper sticker at the end of one of these.
posted by Metroid Baby at 10:06 AM on March 25, 2011 [1 favorite]

> I havn't seen the new TRON movie yet, since I heard it sucks.

Oh, it did suck, but it was a likable form of suck that was pleasant to look at and had a nice veneer of Zen conceit. It was a marked contrast to Avatar which was kind of insulting to look at and was full of heavy handed moralizing, plus it had a scene with Daft Punk DJing a bar fight. It's fun!
posted by Burhanistan at 10:07 AM on March 25, 2011 [1 favorite]

Oooh, sweet. That first link is a doozie.
posted by nickyskye at 10:13 AM on March 25, 2011

> I havn't seen the new TRON movie yet, since I heard it sucks

It's amiable fun of little lasting value, and if you're of a particular age you'll appreciate the numerous callbacks to an earlier era of gosh-wow personal computing and the fact that IT DOESN'T MESMERIZE YOU WITH ITS HORRIFIC, UNCEASING TRANSMOGRIFICATIONS BEFORE BURROWING INTO YOUR BRAIN so yeah, I'd say check it out when you want to kill two hours.
posted by ardgedee at 10:25 AM on March 25, 2011

One badass fucking fractal.
posted by shiu mai baby at 10:56 AM on March 25, 2011

The exotic one looks like cauliflower, then an overstuffed quilt. Not scary, comfy.
posted by Cranberry at 11:00 AM on March 25, 2011

When I finally got my eyes trained properly on this stereo version it was transcendental. The space really feels huge.

It used to take me all night just to render a good old 320x200 Mandelbrot.
posted by Wolfdog at 11:50 AM on March 25, 2011

Can someone explain to me what exactly is going on when the Mandelbulbs appear to be morphing? Are they not actually (theoretical) solid objects? Are they being rotated through another dimension or something?

Fractals usually have some parameters that you can tweak to produce unique (but related) shapes. Cycle this parameter and you get a cool morphing shape for a video. You can play around with the parameters using FractalLab.

For 4D fractlals, such as logicpunk's link, you project it down into 3D, like projecting a shadow onto a wall. The parameter that you can tweak is the 3D hyperplane onto which you project.

My favorite of the videos above is the Mandelbox.

Also, these fractals are rendered approximately through a technique called raymarching. So even in the videos where the shape is static, you'll often see some shimmering and shifting pixels as the camera moves.

Somre more info on the Mandelbox.
posted by Herschel at 12:13 PM on March 25, 2011

A couple of weeks back there was a post here on the blue about the form categories that underpin human hallucinations. I started to post about the tripartite clockwork breathing mechanism that represented the fundamental interactions of the universe that I saw once, but I deleted the post.

Now, go to the first link, surface detail, and imagine it to fill your view, instead of being a portion of a dodecahedron. Mentally center a primary vertex in the center of your view; now animate, and instead of going in one direction, go back and forth, like a pendulum in the Z axis, away from you, then back towards you. And with each swing of the pendulum, the forms change, but they change in Mandelbrot fashion - they make sense, seamlessly morphing.

And on top of that, the forms are quite distinctly clockwork-like, you might even say steampunk.

That's what I saw. Every time I closed my eyes and tried to sleep. I can still see it.
posted by Xoebe at 4:29 PM on March 25, 2011

OK, here is what I understand of the math.

Regular Mandelbrot is made by taking every number on the complex plane, adding it to its own square... then taking THAT number, squaring it again, and adding the original number... then again on and on until it either goes to infinity or doesn't. If it doesn't, the original number is part of the Mandelbrot set.

Julia sets are, I think, made by using some exponent other than 2.

So when you remap that onto three dimensions, I guess you'd basically be layering a bunch of Julia sets on top of one another.

'Zat right?
posted by LogicalDash at 6:28 PM on March 25, 2011

The video labeled as work of Rena Jones was done by Phidelity (Kris Northern). Rena Jones is the author of the song Open Me Slowly that is used as the soundtrack.
posted by Rhomboid at 2:33 AM on March 26, 2011