You may think it's a long way down the road to the chemist's, but that's just peanuts to the Mandelbrot

September 3, 2010 3:42 PM

Last Lights On - a zoom down into the Mandelbrot set to 6.066 e228 (2^760)

Longer Vimeo and downloadable version here. Mandelbrot set tutorial.

posted by fearfulsymmetry (29 comments total)

Wow. Watch that video, then immediately close the youtube viewer: suddenly the MeFi page looks like it's all shifty and . . . weeeeiiiiirddd.
posted by Think_Long at 3:48 PM on September 3, 2010 [2 favorites]

What's amazing is that this has always been here...just waiting for us to develop enough computing power to visualize it.
posted by rocket88 at 3:53 PM on September 3, 2010 [1 favorite]

The effect is better with this, Think_Long.
posted by griphus at 3:55 PM on September 3, 2010 [1 favorite]

Anyone know where I can score some acid to go with this video?
posted by mek at 3:57 PM on September 3, 2010

I can see my house from here!
posted by TwelveTwo at 4:00 PM on September 3, 2010

So that's by far the deepest zoom I ever saw. But I have a technical question - which is, how do we know what we're seeing is the real thing?

This is an awful lot of zoom - how do we know that successive round-off errors in their code don't result in it not being right!? Checking the site doesn't make it clear, though he's pretty damned serious about his fractals...

Wow, 6 MONTHS to render, that's pretty serious. I hope he has some way to store state so if his power goes out... !

The most fun part I always remember is that the Mandelbrot set, the black part is simply connected, which is quite a strong condition, one that means that any area of black you see must have a path entirely made of black into the central region (even if that path appears at a level of magnification way below the one you are looking at).
posted by lupus_yonderboy at 4:00 PM on September 3, 2010 [1 favorite]

[bubble bubble bubble] Math is the shit... [cough, cough] man. [more bubbling]
posted by Jon_Evil at 4:01 PM on September 3, 2010 [1 favorite]

Huh. I wonder how they managed to find that point at the end where it seemed to be going into a repeating pattern of these circles that had these 'spokes' that kept increasing in number. It seemed obvious they were going right for the center of those concentric circles (I don't want to spoil the end, though). There are probably lots and lots of points like that, but they obviously knew what they were going for.
posted by delmoi at 4:06 PM on September 3, 2010 [1 favorite]

This is an awful lot of zoom - how do we know that successive round-off errors in their code don't result in it not being right!? Checking the site doesn't make it clear, though he's pretty damned serious about his fractals...

There's a video of a 3-D fractal where they warn in advance that it gets jerky towards the end due to running out of procressing, so if they are up front about that I'd be reasonably confident about other stuff
posted by fearfulsymmetry at 4:07 PM on September 3, 2010

Obligatory Jonathan Coulton version.
posted by ZsigE at 4:10 PM on September 3, 2010

Nuts! I didn't realize goys love Mandelbrot so much.
posted by gman at 4:11 PM on September 3, 2010

This is an awful lot of zoom - how do we know that successive round-off errors in their code don't result in it not being right!? Checking the site doesn't make it clear, though he's pretty damned serious about his fractals...

Well, to my admittedly ignorant way of thinking, what you see at the end of the video seems rather unlikely to be the result of cumulative errors.
posted by smcameron at 4:12 PM on September 3, 2010

In the early nineties, there was a brief fashion for fractals in book covers and whatnot, so I first saw a Mandelbrot set around the age of 12. Therefore, I will never be able to look at one without seeing a butt. Beautiful, scientific, infinite, chaotic -- butt. Sorry.
posted by Countess Elena at 4:13 PM on September 3, 2010 [1 favorite]

I can't comment on the technical comments because I not a technie. All that I know is that I really thought that was cool. Someone invested a lot of time to put it together obviously. Thanks to them!
posted by Life_Settlement_Broker at 4:13 PM on September 3, 2010

So that's by far the deepest zoom I ever saw. But I have a technical question - which is, how do we know what we're seeing is the real thing?

It wouldn't be that hard to generate it correctly... so why fake it?
posted by phrontist at 5:22 PM on September 3, 2010

how do we know that successive round-off errors

I'm assuming a lot of numerical analysis goes in to writing an app like this...
posted by phrontist at 5:23 PM on September 3, 2010 [1 favorite]

I strongly recommend watching the tutorial linked in the OP. I'm shocked at how simple the math is behind the generation of these images. As they say in the tutorial, it's about sixth grade level. I find these images so much more compelling now that I understand what I'm looking at.
posted by funkiwan at 5:49 PM on September 3, 2010

Neat - there were quite a few patterns in here that I hadn't seen before in fractal zooms, like the swirly spirals and squarish things (as you can tell, I'm not a mathematician). And I was not disappointed in the ending!
posted by Quietgal at 6:09 PM on September 3, 2010

See also: Mandelbox.
posted by Rhomboid at 6:26 PM on September 3, 2010 [1 favorite]

Do your own Mandelbrot zooming!

Download xaos.exe from cnet.com. It's a self-installing Windows app that lets you do your own zooming. It's only 1.5 mb.

Click it after installing, and it starts with the familiar Mandelbrot bubble. This is fast and fun to use, but of course it's not as accurate as the 6 month calculations.

Run it full screen. Just hold the left mouse button to zoom in, and move the mouse to steer the zooming point. The right mouse button zooms out.

It gets rounding errors and fuzzes out after some pretty long zooms. Try the nodes on the long tail on the left side for some good examples. I like to zoom way in, then zoom back out, and see all the details repeatedly shrink to a dot and disappear.

Some settings to try:
Calculation-->Iterations: It starts with 170 iterations. Try 500 or more, and it takes longer, but there's more detail.

UI-->Zooming Speed: It starts with 1. Try 3 or 5 for a fast zoom, especially when zooming out.
UI-->Ministatus shows the zoom level in the corner.
UI-->Autopilot picks a random route to zoom in on.
posted by jjj606 at 6:54 PM on September 3, 2010 [2 favorites]

I missed the download link:
http://download.cnet.com/GNU-XaoS/3000-2053_4-10852924.html
posted by jjj606 at 6:55 PM on September 3, 2010

That's god, right there: emergent systems.

GTAC; 3+/4; Zn^2+c; e^2/hc; ...
posted by seanmpuckett at 7:37 PM on September 3, 2010 [1 favorite]

i'm sorry .. what?
posted by lester at 7:50 PM on September 3, 2010

Goes well with Hendrix.
posted by adamvasco at 3:00 AM on September 4, 2010

Bah far from the deepest zoom... once I was zooming really deep and one node resolved into this perfect blue sphere with wisps of white just like clouds. Zooming through the wisps I saw a continent like thing, deeper a coastline, then to a small house like thing, then into a window and it was an image of me at a fractal computer zooming still deeper...
posted by sammyo at 5:19 AM on September 4, 2010 [2 favorites]

Somehow this reminds me of last year, walking the Highland Way, when I pitched my tent at a little spot on a cliff overlooking Crianlarich and smoked some 5-meo-DMT this dude had given me at a festival. At dusk I heard the sound of a motorbike, reverberating round the glen, appearing at Tyndrum and disappearing west past Loch Lomond, which took two or so minutes. During that time the bike covered the distance I had walked the past three days. Then I thought about stopping at one point and taking a microscope to one of the plants there, and going infinitely deeper and deeper. When I told a friend about this thought later, he claimed this had something to do with Zeno's paradox. (Not sure if I get it, but it seems neat.)
posted by yoHighness at 8:51 AM on September 4, 2010

adamvasco: Goes well with Hendrix.


I believe you; but as it happens I was listening to Pandora, specifically the cuts "Lucky 7" from this album and "Pennants" from this one, and they couldn't have been a more perfect fit.
posted by Greg_Ace at 3:36 PM on September 4, 2010

[I love jjj606's instructions for DIY Mandelbrot-zooming, but having tried it a little I hasten to add that this SourceForge page for Xaos is almost certainly a better place to download the program, not least because it isn't program-specific – that is, there, you can download Xaos for Windows, Mac, or Linux.]
posted by koeselitz at 1:57 AM on September 5, 2010

Thanks so much for this... Although I remember the "hurr cool fractals" from college, I never really caught on to exactly how inherently weird this is. The tutorial is excellent. Can't wait to read more about this. If the set is truly infinitely deep, then why wouldn't you one day come across an image of a monkey at a typewriter, and zooming onto the page, the words of Shakespeare?
How about this: If M-Theory or multiple universes is correct, does the mandelbrot set look the same in them? Seems it would, unless the square root of negative one could somehow be different elsewhere. See what I mean? This is Weird.
posted by joecacti at 4:56 PM on September 5, 2010