On May 22nd, 1998+3, I happened upon Blatte's Pages, a site that has compiled several galleries of fractal art and backgrounds from 2002 to 2012. I thought they were very cool and wanted to try making some of my own.
These were made on the WebPC with Ultra Fractal 2.05, and saved in PNG with a 1024x768 resolution. They aren't quite as nuts or polished as those, but I had a lot of fun playing with the program.
If you want to see more of what it and other fractal art programs can do, check out Apophysis Images, too.
Made in Ultra Fractal 3.05: