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). A reference will be very helpful.

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