Fractals in the World

[Kanamori]

What are some of the ways fractals are used or appear in the world? (Kinda for a school project for extension of mathematical knowledge into the real world). E.g., how the US military distinguishes natural land from man-made building by comparing fractal order. Also, I would imagine using a sphere somehow or possibly other figures like a cube, etc., but how does one determine the fractal order of some three-dimensional object?

[The_Doctor]

What is a fractal?

I am pretty good at maths, but I do not think I have ever heard of a fractal.

Is it an American thing?

[Big_John]

not sure about uses.. but some examples of fractal patterns that "appear in the world" include:

- plants.. leaf, branch and root development can all be described in terms of fractals. fern fronds are a specific example that comes to mind.

- nautilus shells (or any natural spiral afaik).

- erosion patterns. a specific example would be the branching of drainage basins. similar bifurcation can be seen in lightning.

- mountains.. any landscape really, can be described by fractal geometry.


honestly i can't think of much that fractals wouldn't work for..


edit btw matinus: fractals (http://www.jracademy.com/~jtucek/math/fractals.html)

[Paul Peru]

Fractals appear most conspicuously in plants such as ferns, cauliflower etc.
Here's something about fractals in erosion:
http://www.forester.net/ecm_0205_fractal.html
The article also explains fractals in general, Martinus.

A fractal is essentially anything that shows self-similarity at different levels of magnification.
It's not an American thing, even though images of Mandelbrot sets tend to have very loud colours.

[The_Doctor]

A fractal is essentially anything that shows self-similarity at different levels of magnification.

Like that glass pyramid in front of the L'ouvr (SP) in Paris.

[Big King Sanctaphrax]

Gah, I'm having trouble getting my head around the idea of something having non-integer dimensions...

[The_Doctor]

Would having a picture with the same picture in it, with the same picture in it, etc, be a fractal?

After reading that article, fractals sound cool. ~:)

[Kanamori]

Fractal art (http://www.fractalarts.com/ASF/galleries.html)

Julia sets (http://www.ijon.de/mathe/julia/some_julia_sets_1_en.html)
(they're the one's that hippies make w/ imaginary numbers)

[The_Doctor]

Cool, they remind me off biology lessons.

[English assassin]

Gah, I'm having trouble getting my head around the idea of something having non-integer dimensions...

Yeah, I read somewhere that the coastline of Great Britain has 1.8 dimensions. (Maybe more, maybe less, anyway, it wasn't "2")

I am still trying to work out how knowing that might be useful one day. Maybe if we see a rise in mathemo-fascist terrorist kidnappings?

[Kanamori]

"I am still trying to work out how knowing that might be useful one day."

The U.S. military uses it help distinguish between buildings and natural landscape, when they are targetting stuff w/ their sattelite images.

[English assassin]

"I am still trying to work out how knowing that might be useful one day."

The U.S. military uses it help distinguish between buildings and natural landscape, when they are targetting stuff w/ their sattelite images.

Right. How many dimensions DOES a Chinese embassy have then?

[ah_dut]

Gah, I'm having trouble getting my head around the idea of something having non-integer dimensions...
You have no idea...my maths teacher was trying to teach me that last year ~D I was 12...

[Kanamori]

The "dimensions" are non-euclidean, first of all.

"Right. How many dimensions DOES a Chinese embassy have then?"

"The topological features of natural terrain (sand dunes, ocean surface, forests) are characterized by irregular shapes whereas man-made objects (missiles, vessels, vehicles) contain regular features with sharp edges and straight lines. A numerical quantity called the fractal dimension, "D", can be computed from an image of natural terrain. If a man-made object is superimposed onto the natural terrain background, the value of "D" changes noticeably. Therefore, an image could be characterized as completely natural or as containing a man-made object by obtaining the value of "D." By placing this processing capability on-board a satellite, the pre-processed imagery could be fused with other sensory information or simply down linked to national and theater-level analysts. Although fractal-like backgrounds can be defeated by cloud/smoke-cover or camouflage, if fused with information from other sensory sources, it can help the analyst or the processing software identify ground based signatures." (http://www.au.af.mil/Spacecast/app-b/app-b.html)

Show me a picture of one, and I can tell you. Buildings have more order than does the landscape. The Landscape still shows the order, though, because it has its base on the same equations that can be used to describe things. The equations have room for lots of variation, based on initial conditions of the variables in the equation, but they follow the same fractal pattern in how they evolve or generate.