Quest for a true 3D Mandelbrot Fractal.
September 14, 2008 12:58 AM   Subscribe

Quest for a true 3D Mandelbrot Fractal - a very nice exploration of Mandelbrot/Julia set fractals in various kinds of 3D space.
posted by loquacious (21 comments total) 20 users marked this as a favorite
Very cool. It's Mandelbrot, however, as far as tags and title go.
posted by lumensimus at 1:07 AM on September 14, 2008

3D Mandlebrot sets are fun enough (so thanks for the link) but beyond some generalization of the idea of iterating a complex quadratic polynomial you have Mandlebrot's original very loose idea of a fractal, which would include such "3D fractals" as clouds and mountains.
posted by twoleftfeet at 1:36 AM on September 14, 2008

Basically a Perlin hypertexture with the texture function being Mandelbrot Set-like,

posted by jfrancis at 1:51 AM on September 14, 2008

Some early clouds and mountains I had the chance to animate.
posted by jfrancis at 1:54 AM on September 14, 2008

Be careful what you wish for - that's all I'll say. My wife and I were given a mandlebrot dinner set as a wedding present, and it's absolutely useless. You can't serve soup in a bowl with a finite surface area but infinite volume - our lobster bisque just disappears completely. The others courses are also impossible to eat, since you can't tell where the plate ends and the gratin dauphinois begins. Our guests just end up staring at their coffee spoons for hours, delighting in the endless play of forms continually revealed through analysis at higher and higher levels of resolution, and no-one tells my wife how lovely her blanquette de veau is.

I keep telling Abigail we must simply get some Wedgewood, but it was a gift from her Aunt, the beastly old hag.
posted by the quidnunc kid at 2:58 AM on September 14, 2008 [34 favorites]

no-one tells my wife how lovely her blanquette de veau is.

I've been meaning to compliment your wife's ragout, but I've been busy with other things. Please accept my apologies.
posted by twoleftfeet at 3:32 AM on September 14, 2008 [1 favorite]

Oh yes, twoleftfeet - "busy meditating on the vast panoply of visual delights that comes with infinite iteration of quaternions," you claim.

But we all saw you ACTUALLY contemplating her ample bosom over the cheese course.

By Jupiter, I have half a mind to petition the Tennis Club to remove you as Secretary - you dastardly cad.
posted by the quidnunc kid at 3:47 AM on September 14, 2008 [1 favorite]

Nonsense, I say! At no time did my gaze ever stray from the trisection of my angles towards the ever so lovely amplitudes of her cosines.

I iterate, and reiterate, gentlemanly members of the Tennis Club: denounce these accusations as the nonsense they are!
posted by twoleftfeet at 4:01 AM on September 14, 2008 [1 favorite]

Piffle! When one magnifies the very words of the culprit, bleated out in his own defence, one sees other, more fanciful sentences, sprouting off each letter, in all directions!

To whit – looked at under higher resolutions, the upper left hand side of twoleftfeet's words "At no time did my gaze ever stray" clearly resolves into the admission: "Under her bulging décolletage, her breasts quiver like a pensive tripe - oh, Abigail, would that I might feast upon your blancmange, my gourmand Aphrodite!"

The villain is clearly not fit to serve the Tennis Club’s administrative needs. I trust the good-fellows of this website will agree.
posted by the quidnunc kid at 4:17 AM on September 14, 2008 [3 favorites]

You have me, my good man. I must confess my love for Abigail has both complex and imaginary parts. The more I see of her the more I see of her. Indeed, we have fractalled many times.

I will resign my position in the Tennis Club immediately.

But I'll join the Cricket Club tomorrow.
posted by twoleftfeet at 4:31 AM on September 14, 2008 [3 favorites]

Oh, blast it, twoleftfeet! You're really a good chap - I guess I've just jolly well gone and thrown it. Do accept my apologies for getting all stuffy, old boy.

To tell the truth, Abigail and I have been having some troubles of late - she caught me ogling Julia's set, which have always been a strange attractor for me. I guess the marriage is on the rocks - so I shouldn't blame you for moving up the Devil's Staircase and putting your Minkowski Sausage in her Cantor's Curtains, so to speak. I guess we're just both typical residents of Koch Island.

Anyone for tennis?
posted by the quidnunc kid at 4:43 AM on September 14, 2008 [3 favorites]

I shouldn't blame you for moving up the Devil's Staircase and putting your Minkowski Sausage in her Cantor's Curtains

Very good of you. I think we have reached a limit to this cycle.

Tea on the lawn?
posted by twoleftfeet at 4:55 AM on September 14, 2008 [1 favorite]

Well played, dear chap. Well played.
posted by the quidnunc kid at 5:32 AM on September 14, 2008 [1 favorite]

There are some neat pictures, but I'd sort of gently advise that trying to figure out what is "the" 3-dimensional analog of the Mandelbrot set is a bit of a fool's quest. That's still not to say it can't be a fun quest, but there are good (technical) reasons why there isn't a clear-cut candidate to play the role of "the 3-d Mandelbrot set."
posted by Wolfdog at 5:38 AM on September 14, 2008

That guy's first approximation sketch looked eerily like a neuron.
posted by Maias at 6:30 AM on September 14, 2008

I didn't understand anything about the math but I liked the pretty pictures at the end. Call me Barbie - I can take it. Once again I'm struck by how often fractals underlie the real world. Romanesco broccoli is probably the ultimate example of fractals in nature (we even call it "fractal broccoli" at my house), but humans also seem to revel in fractal-like forms.

The fractal cities rendered by Stefan Vitanov are quite reminiscent of Borobudur, a 1,200 year old Buddhist temple in Java (stock images here showing the repeating units of sculpture used all over the structure). Of course Vitanov has undoubtedly seen Borobudur and may have tweaked his rendering to evoke a similar look, but the architects who designed Borobudur had no formal knowledge of fractals. Nevertheless, they came up with a fractalicious design.

David Maldin's Sierpinski Temple similarly evokes Jain temples. (In Rajasthan I saw some Jain temples which were much more blocky and not so ornate, but unfortunately I can't find pictures of anything in this style. They were strikingly similar to Maldin's art.) Again, Malding may have taken his inspiration from previous architects, but those architects worked in a fractal style without the formal mathematical framework.

Any idea why South/Southeast Asian architects developed this style? Something in Buddhist/Hindu/Jain philosophy? Or do architects everywhere like repeating elements, and it's just more obvious in places where the overall style is more ornate?
posted by Quietgal at 11:28 AM on September 14, 2008 [1 favorite]

Quietgal: Ron Eglash wrote a book (and held a talk at Ted) about fractals in African architecture.
posted by you at 11:51 AM on September 14, 2008

Edit requested for changing Mandlebrot to Mandelbrot. Sorry about that. I was tired.
posted by loquacious at 12:57 PM on September 14, 2008

Cool! Some of my work was linked in the article. I'm very interested in the 3D fractal thing but mostly from the IFS side of things (Iterative Function System) using 3D models as Stefan Vitanov does with his Sierpinksi cities in the program Xenodream. (which by the way geeks me out like nothing else)

I have three links which might be of further interest to people who enjoyed this
an animated 3D IFS fractal video
Exploring Pythagoras Tree Fractal in 3 Dimensions

and exploring Sierpinskis' triangle in 3D and sacred geometry
posted by phidelity at 3:13 PM on September 14, 2008 [2 favorites]

I think I made one of those out of Bisquick once.
posted by louche mustachio at 9:30 PM on September 14, 2008

Huh. No one's mentioned quaternions, 4-D fractals yet? I've thought about pulling slices out of one & painting my walls with it. Then I realize that headaches might be the best case scenario there.

The worst case is, of course, awakening the Ancient Ones.
posted by Pronoiac at 12:49 PM on September 15, 2008

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