The beauty of fractals

A friend of mine told me a few years ago that instead of a classic desktop background, he prefers a fractal image. I had no idea what a fractal is and I didn't give it to much attention. After a while I saw a book about fractals. The colorful drawings on the cover drew my attention :) I started to read it and I remained astonished. The complexity that a simple mathematical function can generate and the beauty of the designs that can come out of that left me speechless. I afterwards realized that I knew the principles of how a fractal works long before. Ever heard of "recursive"? It's a programming term used when a function calls on itself. That's mainly how fractals work. They repeat the same function a number of given times or, if you wish, an infinite number of times. But that will most surely crash your computer eventually. This way the pattern it draws is the same every time, but the position, size, direction, color or other attributes it has may differ.

So what is the definition of a fractal anyway? Well, according to Wikipedia, a fractal is "a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole". Got that? To put it simple, if you zoom in on a portion of a fractal, no matter how many times, you see approximately the same pattern, over and over again. Voila. The best graphical representation of infinity.

The term of "fractal" was given by BenoƮt B. Mandelbrot, also known as the "father of fractal geometry". One of the most popular fractals bears his name, the Mandelbrot set.

Fractals also seem to be present in nature, but they are an approximate and finite form. You can find them in clouds, snow flakes, crystals, lightning, ferns, broccoli, cauliflower and even blood vessels.

But what are they good for, other than beautiful and colorful graphics? They're good for a lot of things. The fact that nature uses them in so many situations proves that a fractal is something that offers great advantages. But they are also used in domains such as art(computer generated, African art, painting), signal and image compression, seismology, computer and video game design, medicine and so many others.

The fractals have been around for such a long time and people have come across constantly. Thanks to the introduction of computers, they are now more accessible to everyone and a real science has developed to study and better understand them. This way we'll see them applied in more and more areas. The possibilities that they offer are endless.


Caenwyr said...

I don't believe you answered your own question: Wat are fractals good for anyway? They're beautiful, that's right, and they're used a lot, but what exactly is the use of fractals? In what way are they used, how do they make life easier?

Stelian Andrei said...

Luckily I'm subscribed to comments on my own blog, otherwise I wouldn't have seen this one. I haven't paid much attention to The Yoboo lately.

To answer the questions you raised a simple Wikipedia search should give a small insight into the use of fractals. Besides the theories that are based on the concept of fractal (amongst which the most famous is the Chaos Theory, from my point of view anyway) these also have many implications in science like modeling complex structures that mimic naturally occurring ones, designing graphs and (predicting) their evolution in time based on different factors and of course many other things. I guess a look at the Wikipedia entry on fractals would give a good starting point on their applications.

I once read (I think) of a image manipulation application that used a fractal function to enlarge images considerably and approximate the pixels so that the image had little loss in quality. But that might be old news.

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