What Are Fractals?

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Many people have seen or heard of fractals, but very few know what they actually are. The answer to the question "What are fractals?" is really simple. Fractals can be anything that contains self-similar images within itself. For example, the human circulatory system is a fractal. If you look at the blood vessels in your hand, they resemble the overall shape that the complete system takes on. We are constantly surrounded by fractals and most don't realize it. The computer generated images on this page are fractals, but they are not the only fractals. Most occur naturally. From this point on I will discuss the computer-generated fractals like those that you will find in the Bare Fractals and Fractal Art sections.

Computer generated fractals are created using fractal geometry. This new kind of geometry dismisses the Euclidean way of looking at the world. A mathematician would tell you that fractals are created at the boundary between chaos and order. To fully understand fractals, one must understand the chaos theory.

The theory states that everything is subjected to so many variables that it becomes almost, but not completely, random. A meteorologist named Edward Lorenz helped to pioneer the study of chaology when he discovered a disturbing fact. No matter how much information he gathered, his weather predictions would quickly fail because there was no way he could use all the variables of the weather. A small change in the location of a sun spot would be amplified until it had a large impact. This is the basis for the chaos theory. No matter how much information one gathers, it is still not possible to make a completely accurate prediction because he can't take into account the endless amount of variables involved or the impact and feedback caused by a slight change in one of the billions of variables.

Fractals are not completely chaotic. They have an order to them that keeps them from being totally chaotic or totally orderly. Benoit Mandelbrot helped to discover the order in fractals. He found the self-similar charactersitics in his fracatal sets.

Fractals can be drawn without a computer. One example of this is the Koch Curve. The Koch curve starts as a straight line. The next step is to add a peak in the middle of that straight line. This can be done forever and create a simple and self-similar fractal. The Koch Curve is demonstrated in the animation below.

The ideas in this article are just the basic ideas of fractals. If you have any questions or comments, visit the Feedback section, or e-mail freecloud@geocities.com .