Fractals

In very simple terms, fractals are geometrical figures that are generated by starting with a very simple pattern that grows through the application of rules. In many cases, the rules to make the figure grow from one stage to the next involve taking the original figure and modifying it or adding to it. This process can be repeated recursively (the same way over and over again) an infinite number of times.
The fractals' growth mechanism can be visualized very easily with a simple example. Start with a + sign and grow it by adding a half size + in each of the four line ends. Repeat the exact same process recursively as many times as desired. We'll call this the Plusses fractal:

for more details :

http://www.arcytech.org/java/fractals/intro.shtml

One interesting property that fractals can have is that of self-similarity. The name sounds complex but the idea is very simple. What self-similarity means is that each small portion, when magnified, can reproduce exactly a larger portion.