If you’re old enough to remember the 1970s, the current popular fascination with fractals probably flashes you back to those halcyon days of big hair and wild imagery. Whatever your age, you’ll enjoy Peter Aitken’s explanation of how fractals work. You can even plug in his Visual Studio demo program and make some fractals of your own.
http://xaos.sourceforge.net/english.php
Try Xaos, which generates fractals in real-time and morphs them based on mouse-input.
Many more open source fractal viewers exist, as well.