The term "Fractal" was invented by a mathematician by the name of Benoit Mandelbrot. Mandelbrot wrote a book in 1977 named "The Fractal Geometry of Nature". He demonstrated that the length of a coastline is infinite (relative to fractal geometry). Later, some mathematicians got together and applied a fractal formula to a X and Y cartesian plane (co-ordinates), assigned colours to the iteration formula, and explored the strange shape they named the "Mandelbrot Set". Computers had advanced enough to generate these images in full colour. 
With the "Mandelbrot Set" formula, it is possible to zoom in over and over again, each time bringing up another image with the same amount of detail.  
The program that is used to generate these images, Fractint, can zoom in to a magnification of 1,000,000,000,000 times. If the "Mandelbrot Set" was blown up to the scale of an image that was zoomed to the most extreme view, it would be 1 billion miles wide, almost encompassing the orbit of Jupiter!  Top

All images here were created with Fractint , a DOS freeware program, which was written by 4 main authors and about 50 contributing authors. It has many features and formulas all contained in an exe file just over 1 Meg. It is a DOS based program but runs well in Windows 95. 
These images are mostly Mandelbrot or Julia sets. Included on this website is a parameter file for those who don't like downloading 10 megabytes. One of these files (fract036.gif) took over 6 hours to generate on a 486. In that case, it would be faster to download it.