What is a fractal? An excellent description of the conditions required for an image to be considered a fractal may be found at Dictionary.com by following this link: FRACTAL. (Look at the second entry)
I intend to post a short explanation of how a fractal is calculated, as soon as I figure out how it's done myself and I feel capable of explaining it to others (heh heh). One common type of fractal uses an iterative formula of the form z = z + c, where z starts out at zero and changes as the right side is evaluated over and over, and where c is a complex number. Then if after a certain number of iterations z has not passed some critical value, it is marked as being "inside" the fractal shape. Otherwise, it is marked as being "outside" the area that makes up the fractal.
What are fractals good for? For modeling real weather phenomena, for starters. Clouds, landscapes, the surface of a body of water...all these and more can be simulated by computers convincingly using fractal equations. This can save a lot of memory, as the computer need only store the formula and a seed value to start the iteration process. This is useful not only for scientific endeavors, but for CGI in movies and the like as well. Plus, they're good for making the brains of your enemies hurt a great deal.
I created the "fractals" on this page using a free program called Fractint. This is a wonderful program. It's got a huge variety of "fractals" (not all are true fractals, but I'm not complaining), a user-friendly help system, and a lot more, including a few pre-installed routines to generate some nice pictures. If you have enough disk space, are willing to spend a few hours learning to use it, and are interested in the first place, I recommend trying it out.
The following are links to some of my favorite images that I've somehow managed to create with this program, for your viewing pleasure. Click on the associated link to see a bigger version. Feel free to download any of these images for noncommercial use. Enjoy!
My fractal pages
Fractals that are most notable for their color
Fractals with patterns, shapes, or textures being the most striking feature
Fractals that are just kinda weird, but no less interesting to look at
My home page. OK, so it isn't really a fractal page. But I've put a link to it here anyway.
