Basically, a fractal is a simple mathematical expression that generates an infinitely complex geometric shape. As you "zoom in" to examine the detail of the geometry, more and more complexity is revealed. Many are self-similar -- a zoomed-in view will reveal a small-scale version of the whole, over and over again -- and still others become wildly different at some point.  There are actually many different types and classifications of fractals and literally an infinite number of possible ways to view any given one.  The resulting patterns are at the same time beautiful and chaotic, organized and random.  In some cases a strange and illogical geometric situation arises, such as in the fractal shown here (called the Mandelbrot set), which contains a finite area bounded by an infinitely long perimeter!

Since the 19th century, fractals have been regarded as merely a bizarre form of mathematics and geometry with little or no practical purpose. However, in the 1970's, the mathematician Benoit Mandelbrot adopted a more abstract definition of dimension than what is generally used in standard Euclidean geometry. He suggested that the fractal must be handled mathematically as though it has fractional dimensions, rather than strictly a whole number of dimensions.

Then in 1987, Dr. Michael Barnsley discovered the Fractal Transform which can detect fractal codes in real-world images and natural formations. This has led to some practical uses, such as fractal image compression which is widely used in multimedia computer applications.

These images were generated using the freeware Fractint, by the Stone Soup Group, an in-depth and versatile fractal program which has been perfected and added-to for many years. You can use the program to zoom in on the fractals, in which case the displayed pattern is recalculated at the higher resolution and new detail is revealed, or to rotate to different angles, generate a 3D map of the fractal or project it onto a 3D surface, and to change the color pallet and even cycle the colors to produce some very dynamic and hypnotic effects.  Literally, an infinite number of possible patterns is possible using even a single fractal type or function.