you really should watch this.

November 2, 2008 10:56 AM

Hunting the Hidden Dimension. You may be familiar with fractals, but in this PBS Nova episode, divided online into 5 parts, fractals go beyond the impossible zoom of the Mandelbrot set. Scientists are using fractals to describe complex natural occurrences, like lava, capillaries, and rain forests. In part 5, scientists measure one tree in the rain forests, and the distribution of small and large branches mirror the distribution of small and large trees. Fractals, it seems, are nature.
posted by plexi (43 comments total)

If there's a programming language to create or describe a universe such as the one in which we exist, it has to include fractal mathematics. It's just so efficient.

Or, put in another way: Dude, God's a fractal. Whoa, trippy, man.
posted by WolfDaddy at 11:08 AM on November 2, 2008

"What else, when chaos draws all forces inward to shape a single leaf."
- Conrad Aiken
posted by ageispolis at 11:17 AM on November 2, 2008 [1 favorite]

Stoner insights form the 90s are great.
posted by Artw at 11:17 AM on November 2, 2008

Once again Science confirms something I already learned on acid.
posted by Liquidwolf at 11:19 AM on November 2, 2008 [7 favorites]

I was hoping for more Jeff Goldblum.
posted by Serf at 11:24 AM on November 2, 2008 [1 favorite]

I watched this earlier in the week - TV programming like this has me hooked; I wish the show could have been ten times as long. For something like this, you can only really scratch the surface when given an hour to present it.

It also makes me ponder the convergence of mathematical branches such as this, and other sciences such as M-Theory. When scientists talk about other dimensions existing outside of our 3-dimensional perception, it makes me wonder about whether some of those dimensions could be fractal dimensions. I mean, why not?

Then again I'm just an armchair spectator with zero training in any of this, and my words go right from my brain straight out my ass.
posted by brain cloud at 11:25 AM on November 2, 2008

I love NOVA - thanks for posting this!
posted by OverlappingElvis at 11:26 AM on November 2, 2008

If you're outside the US, look for a bay with pirates in it.
posted by CautionToTheWind at 11:27 AM on November 2, 2008 [1 favorite]

In part 5, scientists measure one tree in the rain forests, and the distribution of small and large branches mirror the distribution of small and large trees.

Erk, power laws. Thanks for reminding me of my thesis, you bastard.
posted by Jimbob at 11:36 AM on November 2, 2008

I wonder which is more potentially irritating: A hippy with a half assed grasp of quantum physics concepts or a hippy with a half assed grasp of fractals.
posted by Artw at 11:38 AM on November 2, 2008 [3 favorites]

If you're outside the US, look for a bay with pirates in it.

Or if you're anywhere, use a net.
posted by WolfDaddy at 11:48 AM on November 2, 2008

I wonder which is more potentially irritating: A hippy with a half assed grasp of quantum physics concepts or a hippy with a half assed grasp of fractals.

You could seek the middle-ground... Be glad someone gives a shit to even half-grasp something of that nature. Unless you'd prefer anyone without a PhD simply defer to "a wizard did it".
posted by Dark Messiah at 11:54 AM on November 2, 2008 [13 favorites]

divided online into 5 parts

each of which is divided into 5 parts,

each of which...
posted by sidereal at 11:55 AM on November 2, 2008 [9 favorites]

Fractals, it seems, are nature.

Headline: Science Vindicates What Millions Had Already Learned from Psychedelics!
posted by treepour at 11:56 AM on November 2, 2008

Forgive me if this is already covered in the documentary, which I haven't had time to watch yet . . .

Make your own fractals with silver christmas tree balls.
posted by treepour at 12:00 PM on November 2, 2008 [1 favorite]

brain cloud: and my words go right from my brain straight out my ass.

Thereby forming new brain clouds! What a fascinating method of reproduction!
posted by ShameSpiral at 12:08 PM on November 2, 2008 [2 favorites]

The world is such a a vast, beautiful place, and yet here we are on the internet arguing on a Sunday afternoon.

Metafilter: What a sad, little life we lead.
posted by ageispolis at 12:14 PM on November 2, 2008 [2 favorites]

It's okay that the show wasn't in more depth and ten times as long — the additional forty-five hours would be very similar to the first five, albeit with slight variations.
posted by adipocere at 12:36 PM on November 2, 2008 [2 favorites]

Google talk from Geoffrey West, one of the guys in the video, about scaling laws in biology.
posted by norabarnacl3 at 12:42 PM on November 2, 2008

Pretty nifty stuff. The part about trees reminded me of Context Free, a recursive graphical design language (previously). In addition to the software, they have a pretty nice gallery of images and their source code.

Changes since it last appeared in the blue:
* Color
* Alpha
* Tiled rendering
* Quicktime movies, SVG output

The result is that it's fairly easy to generate biological looking structures using self similarity.
posted by pwnguin at 1:10 PM on November 2, 2008 [1 favorite]

I'm with Wolfram on this. :) Fractals don't create life, life (and other matter and energy distributing processes) create fractals.
posted by aeschenkarnos at 2:21 PM on November 2, 2008 [1 favorite]

Neither Artw or I said anything about it being something only for mathematicians or physicists, and I personally think the opposite — the study of fractals for their own sake is almost exclusively 'for' interdisciplinary hand-wavers. Anyone who can use the words 'chaos theory' without a lot of ironic inflection and audible shrugging is not worth listening to.

Anything that divides or multiplies tends to exhibit self-similarity. While that might make a good whoa moment for the intoxicated or teenage, it's not a particularly productive insight.

There is plenty of good work to be done in pure mathematics (Group Theory, et. al.) that in the early nineties would have been presented in terms of fractals and automata. Eventually everyone figured out that Stephen Wolfram was full of shit, and people got funding for their work by couching it in the language of String Theory. As terrible vibrating string metaphors wear out their welcome, grad students will move on to something else.

Any scientific field that gets the attention of the popular press tends to be dragged down by all the superficial attention. You know how the NYT Style section is constantly publishing big flashy articles about expired trends that somehow always miss the point? The Science section is no different.
posted by blasdelf at 2:29 PM on November 2, 2008 [3 favorites]

Eventually everyone figured out that Stephen Wolfram was full of shit...

O RLY?
posted by chillmost at 3:09 PM on November 2, 2008

[sorry folks to "fuck you guys" talk pretty much needs to go to email or metatalk. don't like the post, fine, don't turn it into attacking other users.]
posted by jessamyn at 3:11 PM on November 2, 2008

From the astral plane, it is impossible to distinguish blasdelf from a hippy. Don't know if that helps put things in a better perspective, but there you go.
posted by Meatbomb at 3:14 PM on November 2, 2008

Eventually everyone figured out that Stephen Wolfram was full of shit
Do share this knowledge, o wise blasdelf ...
posted by aeschenkarnos at 3:17 PM on November 2, 2008

O RLY?

YA RLY. His book has the highest quality sets of voted-up reviews I've seen on Amazon, few of them favorable to him. Common themes include: "Not new, not science, or not Wolfram", "A new kind of" ravings, and using his theories to tear apart his work.

This review sums a lot of it up, and contains a gem that better exposits my criticism of this post:

"This brings me to the core of what I dislike about Wolfram's book. It is going to set the field back by years. On the one hand, scientists in other fields are going to think we're all crackpots like him. On the other hand, we're going to be deluged, again, with people who fall for this kind of nonsense. I expect to have to waste a lot of time in the next few years de-programming students who'll have read A New Kind of Science before knowing any better."

posted by blasdelf at 3:54 PM on November 2, 2008

blasdelf, from what I understand the critical reaction has been along the lines of "Hey, most of this isn't particularly new. And wow, quite the ego there." I'm not going to get into those *non-scientific* concerns. But I don't think there are many people who are prepared to say that all of the intriguing work done on cellular automata and their ilk in the past few decades amounts to "shit." There's still a long way to go in this area, and I suggest you wait a few more decades before you make astonishing statements like this.
posted by naju at 4:34 PM on November 2, 2008 [1 favorite]

My mom recommended that I watch this and it annoyed me because it was like a person jumping up and down screaming "fractals fractals fractals". Also: didn't mention Adrien Douady at all.
posted by oonh at 4:49 PM on November 2, 2008

I don't think I like the idea of judging the merit of a scientific book based on Amazon reviews.
posted by empath at 5:15 PM on November 2, 2008 [1 favorite]

That said, this kinda sucked. Nothing new or particularly interesting or insightful, not even a good general introduction to the topic, IMO. Why totally ignore chaos and unpredictability?
posted by empath at 5:18 PM on November 2, 2008

empath: The thing is, it's not a scientific book! (and many of the reviewers are tenured academics). Here's another collection of reviews.

naju: The "not science" concern is pretty important — much of Wolfram's original work is syllogistic at best and often straightforward in it's falsehood. Even with all the repetitious ego and wallpaper stripped out, it would have been torn to shreds in peer review.

I haven't seen much "CA for it's own sake" stuff that wasn't either Wolfram-style totalizing BS or dilettante fractal-zoomer wallpaperism.

There's been plenty of compelling work that just happened to peripherally involve CA, but it is overshadowed by the pop-sci. One of my old roommates was working on biology simulation research using CAs in Logo, but he had a hard time convincing non-laymen (including myself at first) that he wasn't a bullshitter.
posted by blasdelf at 5:29 PM on November 2, 2008

It was telling to me that scientific skeptics of fractal theories were given a few throw-away mentions, never by name, never explaining why, never given a voice. I *like* fractals, and will freely admit that they're all over the place. The problem is, that they are often invoked reflexively, simplistically, even in cases where self-similarity is highly unlikely. There are other sources of complexity in nature. Some of the specific examples of modern fractal applications in science were cases that I was previously familiar with, and have heard seemingly valid criticisms of. It's frustrating to see such a sweeping one-sided description of a science topics, particularly because there are plenty of non-controversial scientific applications of self-similarity. Fractals are cool, even if you're honest.

Full disclosure: my graduate research group was partially devoted to arguing against certain fractal invokers.
posted by Humanzee at 6:35 PM on November 2, 2008 [3 favorites]

Fractals in nature are pretty obvious.
posted by Mach5 at 6:50 PM on November 2, 2008

There are other sources of complexity in nature.

I don't know much about it, but "similarity" is pretty general, right? Can't I just say "similarity under some transformation", and thus turn any recursive relationship into a conceptual fractal? Then, since you can do anything with recursion, can't I describe every source of complexity as a fractal? OK, probably not, but I guess I just want to know why not, or why it's not necessarily useful to think in those terms.

Some of the specific examples of modern fractal applications in science were cases that I was previously familiar with, and have heard seemingly valid criticisms of.

If you could dig up some of those criticisms and link to them, I would be grateful.
posted by Xezlec at 7:43 PM on November 2, 2008

Fractal isn't just "similarity under some transformation", but specifically similarity under scaling transformations. A very simple non-fractal form would be segmentation, which is ubiquitous in biology. A more complicated non-fractal form would be something like the brain, which is highly structured. Some parts of it are similar to other parts (e.g. the cortex contains many columns, which have a similar gross organization to them) but it isn't strictly segmented even in the cortex, because the connections and various subtle features vary across the cortex. And there are non-cortical structures which have little similarity to the cortex ---different cell types, organization, synapse types, etc. This is because the role of the brain requires various trade-offs, including a trade-off between function and simplicity and robustness of construction. These types of trade-offs are common to nature, as well as to engineering in general. Thus there is a common type of complexity in nature that is much more akin to the complexity of an engineered structure than a fractal. Natural structures often have parts that are different in highly specific, information-rich ways (a fractal has superficial complexity, but can be described very simply).

One problem with research in complexity is that fractals tend to produce certain kinds of statistics, called "power law distributions", which were referenced upthread. However, so do other non-fractal complex processes. All too often, the presence of power-laws is taken to indicate self-similarity (I don't mean to accuse anyone specifically of that here, only to point out that it *does* happen). Therefore when someone cries "fractal" and it's not *obvious* that they're right, I like to see reasoning, and hear any skeptics.

I'd like to fulfill your request, but I can't Instead I'll give you a vague description and an excuse. I didn't personally study anything directly referenced in the documentary. I talked to a professor who mentioned the fractal-heartbeat people, and had the criticism that the heartbeat is regulated in a manner tied to many other physiological processes, which all vary based on past and present activity (e.g. breathing, what you ate, moving around, talking, etc). Thus much of the variation observed in heartbeat may be attributed to the lack of controls on a healthy human, rather than anything really deep about the heartbeat. I don't necessarily believe this myself (although it sounds reasonable to me) but I would have liked to see a little back and forth. You know, science. Instead we get the sales department. My excuse for not linking anything, is that everything I've seen that touches on the subject is in scientific journals, which I can't access from home (thankfully I'm not at work late at night on a Sunday), and would be useless to you anyway, unless you happen to have internet access at a university.
posted by Humanzee at 8:35 PM on November 2, 2008 [2 favorites]

Thanks, Humanzee, you answered my question just fine. Actually I do have internet access at a university, but I don't really think I need a Journal citation anyway. I'd probably just stare at the article with a confused look.
posted by Xezlec at 8:43 PM on November 2, 2008

I talked to a professor who mentioned the fractal-heartbeat people, and had the criticism that the heartbeat is regulated in a manner tied to many other physiological processes, which all vary based on past and present activity (e.g. breathing, what you ate, moving around, talking, etc).

Vaguely familiar with this area, as I did some work about a decade ago on cardiac arrhythmias. The fractal proponents aren't saying that the heartbeat is purely a fractal, but is when all other inputs are held constant. One of the characteristics of recursive functions is that changes in the parameters can swing regular appearing sequences into "chaotic" sequences, and so the hope was that by identifying both the underlying recursive relationship and the parameter support region leading to chaotic behavior, one could cure or prevent fatal arrhythmias. The promise of reading and correcting the parameters through the use of implantable sensors/pulse generators was the prize sought. I've been outta the game now for 10 years and have no idea where it stands now. A few data sets I did work with were somewhat convincing, but, you know, measurement error and all.
posted by Mental Wimp at 9:49 PM on November 2, 2008

Xezlec, here is a more recent example (sorry, abstract only).
posted by Mental Wimp at 9:55 PM on November 2, 2008

A more complicated non-fractal form would be something like the brain, which is highly structured. Some parts of it are similar to other parts (e.g. the cortex contains many columns, which have a similar gross organization to them) but it isn't strictly segmented even in the cortex, because the connections and various subtle features vary across the cortex.

I would think that examining the differences between the brain as it actually is and how it would be if it were simply fractally generated would be useful for understanding how the brain functions; to help separate actual complexity from apparent complexity.
posted by empath at 10:36 PM on November 2, 2008

A terrific layman's book about this kind of thing (and more!) is Philip Ball's The Self Made Tapestry: Pattern Formation in Nature which I read last year and can't recommend highly enough.
posted by wobh at 11:27 PM on November 2, 2008

Mental Wimp: thanks, I think you've just about doubled the number of sensible things I've heard on the topic. That said, I think my professor's claim was that it wasn't possible to hold the inputs constant without killing the patient first. I don't know how much expertise this guy actually had though. I think a little back-and-forth from the people slugging it out in the trenches would be very illuminating.

empath: I was a little unclear earlier. I meant that the brain's gross structure is somewhat segmented, and not at all fractal. I actually got into the brain business via complex systems. My graduate group tended to pick fights with a specific subset of the fractal crowd, and some of them were claiming the brain was fractal. Eventually I realized that pretty much no one cared what these guys thought, and that arguing over this stuff wasn't going to advance my career or teach me anything. My inclination now is to become detail-oriented. If you're trying to understand how sub-cellular machinery affects neuron and network activity in a non-brain ganglion, some guy telling you that the brain is fractal seems pretty irrelevant.

Perhaps amusingly, my next project is likely to involve analysing the structure of dendritic branching. Which sure looks fractal. That's just to say, I don't reflexively hate fractals.
posted by Humanzee at 5:04 AM on November 3, 2008

I haven't seen much "CA for it's own sake" stuff that wasn't either Wolfram-style totalizing BS or dilettante fractal-zoomer wallpaperism.
The most famous theorem about the (generalized) Lights Out puzzle is proven by a "garden of eden" type CA argument.
posted by Wolfdog at 11:18 AM on November 3, 2008