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: 1) changed 'iterated maps' -> iterated functions systems
      2) a similar question was asked [here][2]
      3) An article suggesting a [counter-example][3] is suggested in the comments below


  [1]: http://www.sti.uniurb.it/events/sfm13ds/slides/edalat.pdf
  [2]: http://mathoverflow.net/questions/74458/is-there-some-known-way-to-create-the-mandelbrot-set-the-boundary-with-an-ite?rq=1
  [3]: http://www.researchgate.net/publication/228394609_A_LOCALLY_CONNECTED_CONTINUUM_WHICH_IS_NOT_AN_IFS_ATTRACTOR?ev=auth_pub