Sorry for responding to this so late, I haven't gone on the forum for awhile.
I guess I should start out by explaining what fractals are. There are many different types of fractals, but they are generally described as patterns or images that are self similar. Self smilarity is when you can zoom in to a part of an image, and that part looks nearly identical to the origional image. Hypothetically you could zoom in to a part of a fractal an infinite amount of times and this would still work, however, it doesn't work with real-world renders of fractals, since these are only approximations of fractals. (Pictures are limited by pixel size, and pysical objects are limited by their smallest particles)
Mathematically, fractals are made up of real and imaginary numbers, making them complex numbers. In fractal art, complex fractal equations are solved many times to come up with a HUGE number of solutions. Since these are only numbers, fractal art software interprets the solutions as colored pixels, rendering them row after row.
To make fractal art using a fractal art software, one usually starts by chosing a complex equation, each haveing certain shapes and patterns unique to it. Next is choosing the rendering, which determines more of the shape and style of the resulting image, followed by choosing the coloring of the image. Then comes zooming in to different parts of the image to find a nice-looking region of the fractal. (This is usually the most time-consuming part, but very beautiful images can result)
I hope that explains the basics of fractals and fractal art a bit.