I know many people don't know exactly what a fractal is...I first saw them when I was in college, but didn't really start exploring and creating them myself until recently. Unfortunately, the answer to the "what in the world is a fractal anyway?" question is not a simple one, but as I'm no mathematician, I will keep it basic.

The term "fractal" is an abbreviation for fractional dimension. A line has one dimension, a plane has two dimensions, and a cube has three dimensions, but a fractal falls somewhere in between--therefore, it's a fraction of a real number, or "fractional." Fractal geometry is a reflecton of nature--mountains, trees, clouds, rivers, and seashells are all examples that have fractal forms.

One feature of fractals is that they are fragmented and "self-similar," which means as you look closely at a small segment of a fractal, the basic shape will repeat itself, smaller and smaller. If you took a magnifying glass and found a tiny section of fractal and blew it up to full size, you could then pick out another tiny area and magnify it...and the detail would be as crisp and varied as the original. Look at the examples below:

Now, those magnifications might not be that interesting, but you can see that the forms stay similar to the original and the detail continues to be sharp, even at such huge magnifications. However, the most exciting thing is that fractal forms are similar, but not always identical. So, by exploring various areas and different formulas in fractals, you can find great shapes.

Because fractals are based on mathematical calculations, computers are a vital part of creating and exploring fractals. Some fractals can take millions, if not trillions, of calculations! Now that computers have become widely available and can keep up with these types of calculations, fractals have gained more popularity.

There are many different fractal generation programs available today. For more details on where to locate some of these programs, visit my software links section.

One point of debate is the artistic merit of fractals, given that the calculations are performed on a computer. I can only say that computers use the data they are given by humans, and it takes a great deal of artistic skill to explore and manipulate a fractal formula to create unique pictures with color, line, balance, and aesthetic appeal. Personally, I fell in love with fractals at first glance and enjoy creating them every day!

If you'd like to learn more about the nature of fractals, I've assembled a list of links to various websites. Some are very technical explanations from math departments and some are in layman's terms. I hope you learn more from them than I am able to give in this basic explanation. Enjoy!

TECHNICAL EXPLANATIONS / DEFINITIONS:

A very good, but technical explanation of fractals and their properties.
http://www.math.okstate.edu/mathdept/dynamics/

An excellent learning resource geared towards elementary and middle school students that is perfect for anyone who needs to know the basics, with lots of visual references.
http://math.rice.edu/~lanius/frac/

A series of lessons from Yale University with many illustrations--starts simple and gets very complex.
http://classes.yale.edu/fractals/

BIOGRAPHIES:

One of the founders of fractal geometry, Benoit Mandelbrot.
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Mandelbrot.html

Another founder, Gaston Maurice Julia, and a good explanation of fractals.
http://www.bath.ac.uk/~ma0etd/fractals/julia.htm

ORGANIZATIONS:

The Fractal Foundation is an educational organization whose mission is to educate and inspire people about mathematics, art, science, chaos theory and nature.
http://www.fractalfoundation.org/