Fractal art (especially in the western world) is not drawn or painted by hand. It is usually created indirectly with the assistance of fractal-generating software, iterating through three phases: setting parameters of appropriate fractal software; executing the possibly lengthy calculation; and evaluating the product. In some cases, other graphics programs are used to further modify the images produced. This is called post-processing. Non-fractal imagery may also be integrated into the artwork. -Wikipedia
Artists who use fractal sets to express themselves are unique in that they work with chance more than any other artist. Mistakes in fractal generation are part of the process of discovering the image you are trying to create. Unlike more traditional art processes, fractal art requires the artist to set parameters and then see what happens. Of course, more experienced artists using this form are able to reduce the chance factor significantly. However, I think it's exactly that element of chance that makes fractal art expressive and strange.
Halos gazeux by claude19
Fractal art is also inherently abstract. There's literally no way to create a realistic scene using fractal generators. And since realism is an accepted "norm" in art, fractal artists must work with their imaginations rather than simply creating a scene from a photo or their memories of a scene in life.
So, two factors: chance and abstraction. These two elements are exactly what drove modernist artists like Pollock, Duchamp and Klee. And their work was deeply rooted in the unconscious, meaning that their work expressed their unconscious drives and fears more than traditional realistic artists.
View from the Beach by philsh
The fractal art gallery at Renderosity.com is a wonderful place to explore this moody and spiky art form. Artists like dochtersions, claude19 and philsh are creating works are fresh and invigorating; a welcome change from the often mediocre, pop-culture-obsessed artists who try to copy the latest popular arts.
The Renderosity fractal art gallery is also quite active. You'll see new works practically every day. It certainly is one of my favorite galleries and is a perfect representative of the art of Renderosity.
Splash Image: Incandescent by miliff
Image #1: halos gazeux by claude19
Image #2: Lenticular Anomaly by ratkov