fractals in nature

Factual Questions
1

I happened to catch a nova special on PBS last week regarding fractals (see more here.

One of the most famous pioneers in fractals is Benoit Mandelbrot, and a lot of folks may remember Mandelbrot fractals as a screen saver on their computers back in the late 80’s and early 90’s.

I won’t go into details on fractals, since I figure folks that click on this thread either know about fractals or will read about them on the PBS link above, or other sources.

One of the fundamental ideas of fractals is that every design in nature is made up of smaller pieces of that same design. So, for example, a mountain is made up of countless mountains of a smaller size. All you had to do was focus in closer to the object to find smaller objects that looked exactly like the larger object. (I know I’m not explaining this very clearly, so please take a look at fractals on the web if you don’t find the info you need on the PBS link.)

Anyway, there have been some fascinating finds with fractals in nature. One of the segments of the NOVA show showed a scientific team that downed a tree, to see if its growth pattern could be defined by (and be consistent with) fractals. After measuring the tree and each of its branches, they found that yes, the tree followed the rule of fractals. Not only that, but based on the layout of trees in the forest around this tree, they determined the trees also followed a predictable pattern. Very interesting stuff.

My question is, has anyone done any research on space, the layout of stars and galaxies in relation to each other, to see if it fits this fractal phenomenon? If so, what are the results? If the results show fractal relationships in space and stars
what in the world does it mean in the larger scheme?

2

I have heard that some clouds have been demonstrated to have self-similarity for ten orders of magnitude – ie, the shapes and proportions observed at full size can also be observed at 10 000 000 000 magnification.

3

my favourite is the Romanesco Broccoli, doesn’t answer any of your questions but it is pretty (but it isn’t as tasty as it is pretty)

4

The cosmic microwave background radiation has some fractal properties, specifically what’s known as a “scale-free spectrum”.

5

One of the early multi-cellular life forms was somewhat fractal in form. I don’t recall its name, but David Attenborough showed an example in his recent special “First Life.”

6

I believe the show specifically mentioned clouds as an example on the show. I don’t remember the numbers, but yes, clouds are also considered to follow the fractal phenomenon (my phrase, not official)

7

Thanks for this link. I’ve never heard of romanesco broccoli, but I assume you could eat it? I’ve never seen that in a grocery store.

I will see if I can dig up anything in my spare time today about space. It sounds like it has shown up in the CMBR link from MikeS, but I’m wondering what significance it has (if any).

The thing I found so fascinating about the tree example was that the scientists could use that single tree to approximate the location of every other tree in the forest. That implies a natural optimization and order to things. I would therefore assume that the galaxies, the stars within them, etc. have to have fractal properties. Of course, I don’t know, and don’t know how you would even study this, which is why I posted in the first place.,

8

Not every design. Fractals CAN yield simple discriptions of may very complex designs. Even then most natural forms are “fractal like”. You can make them look even more natural by following fractal rules and throwing in a few random errors.

One application NOVA missed is fractal based wavelet compression of audio and video data. Basically the waveforms are analyzed as the some of fractal (wavelet) curves, rather than sinusoids. The compression ratios are spectacular, but the process is extremely computation intensive. Given that mathematics have had only a couple of decades to work on this, there is hope that faster methods will be discovered…if not, it is looking like brute force computing will come to the rescue anyway.

9

Absolutely, it is a fairly common addition to our weekly veg box when in season.
It is wondrous to behold up close.

“stop staring at dinner” my wife once said.

The only downside is that it tastes just like cauliflower, which is fine if you like that sort of thing but I only really eat it out of novelty value.

10

Not surprising as they are the same species.

11

You can, but it tends to repeat on you.

12

Nobody’s addressed the question in the OP:

So here is Wikipedia on Fractal Cosmology:

Lotsa references to original papers at the end.
There’s this, too:

13

(shakes head)

14

Hah! My boyfriend *just *showed this to me last night when we were grocery shopping; I’d never heard of the stuff before. I was coming into the thread specifically to talk about it, since the title suggested it might be appropriate. :smiley:

15

Scale-free networks show up all over the place and are fractal-ish.

16

One needs to be careful of some claims about deep fractal natures. There has been some level of overclaiming, and some rather dubious use of the fractal metrics to prove relationships.

For any physical process there are scale limits of the process that will stop the fractals. The cloud example is where turbulent flows do have some level of scale invariant structure - but even these are clearly limited by the Reynolds number at small scales and the maximum size of a cloud at the larger. Systems of clouds are not cloud like.

Taking a physical entity and attempting to extract a fractal characterisation is something to be done with care. If you have a hypothesis as to the nature of the fractal you can look for that form of self similarity. However there are simple algorithms that just blindly go looking for something that has some amount of “fit” at varying scales and attempts to extract the fractal coefficient. These algorithms are known to be easily fooled, and there are times when no credible fractal mechanism exists but a fractal dimension is found. Claims for fractals in some geophysical processes are very dubious.

Probably the biggest sin is confusing a power law distribution with fractal nature. A fractal nature will exhibit a power law in measured distributions. But the presence of a power law distribution does not imply a fractal nature.

A fractal nature really implies that you can identify the same structuring mechanism at work at different scales. The trees in a forest example is extremely dubious. It implies that if I found a tree with a different fractal dimension, that the physical distribution of that species of tree in a forest would be both different, and could be predicted from the morphology of that species in some mystical manner. Some of the claims about fractals cross the border into mysticism.

17

So are kale, collard greens, Brussels sprouts, cabbage, and kohlrabi, but they don’t taste much alike. Plants is weird, Brassica oleracea especially.

18

I’ve never seen in a supermarket, but the two places I have were both farmer’s markets: Pike Place Market in Seattle and the Jean-Talon Market (actually called Marché Central).

19

Just saw it at Pick 'n Save last night, so supermarkets definitely carry it. IIRC it was termed slightly differently than “Romanesco broccoli,” though.

20

You could be right here. The tree example was a singular example in the show. And now that I’m thinking about it, I don’t recall if they said the fractal pattern of the one tree would reflect the entire forest or a section of the forest around that tree.

However, the proof they showed was indeed convincing to me, and apparently to the other scientists and mathematicians on the show. If these folks are merely jamming a square peg into a round hole to give the field of fractal study some credibility, I don’t know.
CalMeacham, thank you for the links.