Thursday, October 11, 2012

Fractal Factories

In my recent research adventures, I've been looking closer at nanotech, fractals, and, as I mentioned a while back, Mars. I'll cover more nano issues in a future post, and I covered some Mars information in a prior entry. On to fractals...

If you are as interested in this field as I am, there are quite a few tutorials and a handful of books out there. There are also some great, well-presented, basic videos here, here, here, and here. Another good starting point is the Nova presentation, "Fractals: Hunting the Hidden Dimension" if you can find it.

The amazing thing about fractal math is that at it's most elemental level, the formulas are relatively simple and based on concept of self-similarity. Where it gets complicated quickly is when those formulas are repeatedly applied.

Fractals have applications in numerous fields and the list is growing everyday. The connections they are finding between this type of math and natural systems is even more impressive. Fractals have been discovered in organ structures (such as the lungs) and in the structure of the circulatory system. Fractals also exist widely in nature, such as in the head of a cauliflower.

One of the interesting applications of all this has been to computer gaming, where mountains, clouds, landscapes, forests, and even planets can be rendered with fractal formulas. The results are often as convincing as the real thing.

So why did I title this post "Fractal Factories"?

Well, one of the more unusual aspects of fractals is the existence of iterated functions and iterated function systems. Essentially, the output of the initial function is fed back into the function. This can go on indefinitely, and some of the results can be visually strange and often stunning. If you have the right software, you could theoretically keep zooming into on a portion of the rendered fractal and it would endlessly reproduce itself. In other words, even if you focused in on a tiny part, it would still resemble the larger whole (self similarity).

Talk about the efficient packaging of information! Like a factory, it can keep on churning out things. Yet, unlike a real world factory, with these types of functions those "things" are copies of itself.

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