The Cryptology of Fractal Geometry

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The Cryptology of Fractal Geometry

Written by Nathaniel Musselman

Art from Nature: The Cryptology of Fractal Geometry

Is mathematics the language of Nature? A recent article presented the philosophical argument that mathematics is the 'cryptographic key' to unlocking Nature's secrets.

http://www.ias.ac.in/currsci/jun252007/1690.pdf

In other words, mathematics has been designed by humanity to interpret our surrounding environment. Fractal geometry demonstrates the elegant and beautiful patterns often found in nature. These patterns can be interpreted and reproduced mathematically by simple or complex equations.

So what exactly is a fractal? A fractal is an object that is self-similar. This means that any piece of the object, when reduced or magnified, will be similar to the object as a whole. An example of self-similarity would be a Koch curve, which is infinitely self-repeating.

http://upload.wikimedia.org/wikipedia/commons/6/65/Kochsim.gif

We can find fractals everywhere in nature from amino acids to entire galaxies. Chaos physicists have even found simple equations to explain chaotic behavior.

http://upload.wikimedia.org/wikipedia/commons/6/69/Bransleys_fern.png

http://upload.wikimedia.org/wikipedia/commons/6/6d/Animated_fractal_mountain.gif

http://upload.wikimedia.org/wikipedia/commons/b/b8/DLA_Cluster.JPG

Mother nature paints a pretty picture, but the math behind it can be just as enticing. Modern artists have taken the fractal to new heights of expression.

http://dreamtreestudio.com/
http://www.willamette.edu/~sekino/fractal/fractal.htm
http://www.wack.ch/artis/kodgal.html

If you want to experiment with your own fractals visit this really cool site:
http://math.rice.edu/~lanius/frac/

Exploring mathematics proves to be an interesting lesson on its own, but at some point math breaks down under the extremes of our universe-revealing our flawed understanding of nature. However, our understanding of nature doesn't appear to be under threat of extinction. Thank goodness!
Enjoy and have fun exploring!!

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