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Fractals

There’s lots of different kinds of sciences. One of the most recent new discoveries is the idea of fractals.

Dictionary.com defines a fractal as a “figure or surface created by successive subdivisions of a simpler polygon or polyhedron, according to some iterative process.” In other words, if I were to take a shape and divide it into smaller, equal parts, all of them would be identical to the whole. This idea suggests that an item can continually be reduced and divided into infinity, but the exact shape will eternally continue to repeat itself in smaller forms.

This idea of fractals has been around for a while, but the term was originally coined by Benoit Mandelbrot in 1975. The science-y part lies in the fact that there is a mathematical equation to understand and construct fractals. The Koch Snowflake is an example of a manmade fractal:

As you can see, the original shape  is a triangle. Then two triangles. Then, off of each point, smaller, but identical triangles are drawn. This process repeats infinitely until you have a different shape that is actually the millions of smaller copies of the smallest shape. The Kock Snowflake is a basic variation of fractals; there are far more complicated designs on the web for your perusing!

Fractals have interested the science community because, not only can they be created mathematically, but they also exist in the real world. Snowflakes are a perfect example:

The same pattern keeps repeating itself over and over. The same is true for the veins in leaves:

Personally, I find it extremely interesting that this tremendous amount of detail and repetition exists in nature. I think it speaks to the tremendous value and importance and relevance of science. But, perhaps, does it allude to some sort of higher power that has not only the scientific capability, but the cerebral creativity to set such amazing examples of precision and complex beauty into motion?

Here’s a video of some fractals. The camera continually zooms closer and closer into an object, and the same shapes keeps repeating! http://www.youtube.com/watch?v=G_GBwuYuOOs

Has anyone heard of fractals? Does anyone know anything noteworthy about them?

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Categories: Uncategorized
  1. October 24, 2011 at 1:48 am

    Fractals are one of the late 20th century’s greatest mathematical discoveries, without fractals there would be no cell phones (antennas use fractal technology), accurate weather predictions (weather patterns follow fractal dissipation), advanced texture rendering (3d rendering relies heavily on fractal polygon division), or image compression (which uses the famous mandelbrot set to compress color images). They provide an essential component to life, infinite complexity. The vastness of the implications of fractals are tough to immediately grasp.

    The unfortunate reality is that although fractals have been widely popularized because of their beauty, few realize their true potential and worth. Fractals are the paragon of efficiency, and emerge through natural selection.

    As such, nature incorporates fractals and the golden ratio (φ= (1+ √5)/2) as exquisitely illustrated in the following video http://www.youtube.com/watch?v=kkGeOWYOFoA (no html allowed in comments, so the link has to be manually submitted as a URL)
    The concept of fractals can be applied in limitless ways, uniting such seemingly unrelated concepts as satellites and origami (as this TED video will show http://goo.gl/n5ld6)

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