Fractal art is traditionally different from regular illustrations. They can be both vector or pixel but usually special programs are needed to create them. The programs are based mathematical formulations and variations. Mathematicians creates the basis of the simple elements and the designers changes only parameters to get artistic result.
Fractals are sometimes most important part of a design. Nowadays they are widely used even by the biggest product releases and campaigns.
Some softwares that you can use, real long and useful list:
Here are some examples of digital fractal art on Dreamstime:
Photo credits: Jan Kolcak, Murat Cokeker, Dusipuffi, Tyler Boyes, Markus Gann, Sovpag, Tomas Marek.