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Proof of im/possibility of constructing any fractal by iterated maps?

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 maps. A reference will be very helpful.

PS: thank you all for constantly asking to refine my statements, I will restate the questions more precisely and post it again.

Ten
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