"Not every photograph is art; not every fractal is art; not every drawing is art. That's not to say that every fractal isn't."
re: The Fractal Universe. (Are fractals art? hq blog, 8/8/11)
[link]*I could come up with an argument related to a dictionary definition of 'art,' but looking, I've found that the definition given isn't consistent across the board. For that reason I'll clarify that my definition of 'art' includes the use of imaginative talent, usually in the use of creative work using technical skills.
In this case, a fractal can be art as much as anything else.... like artistic carpentry, or architecture.
As for whether any specific, individual piece can be called art- I couldn't say. I suppose it would depend on the creative process of the author - and by the same definition, can you really say that all portraiture is art, either?
*There are too many ways to define 'art':
/n/ The expression or application of human creative skill and imagination... the quality, production, expression, or realm, according to aesthetic principles, of what is beautiful, appealing, or of more than ordinary significance... A re-creation of reality according to the artist's metaphysical value judgements... Activity intended to make something special.