Well the question is as simple as that and what I really want to see is if there is a mathematical proof that can tell whether every fractal(object of any non-integer dimension) can be constructed by iterated function systems(such as in p.55 of [this][1]). A reference will be very helpful.

EDIT: changed 'iterated maps' -> iterated functions systems


  [1]: http://www.sti.uniurb.it/events/sfm13ds/slides/edalat.pdf