Iterated function system of a compact set.

Question

This is a reference request and so I'll be skimpy on definitions, unless asked.

A well known result in fractal geometry says that given an iterated function system (IFS) $\{S_1,...,S_m\}$, there exists a unique attractor for this IFS. i.e. a compact set $F$ such that $$F=\bigcup_{i=1}^m S_i(F)$$

Reversing this picture, suppose you have a compact set $F$, does there exist an IFS whose attractor is $F$?

I'm requesting references on:

1. Given a compact set $F$, under what conditions (on $F$), does there exist an IFS whose attractor is $F$?

2. If an IFS does exist, can we explicitly write it down?

Probably relevant: There is an approximation result that finds an IFS whose attractor is within epsilon distance from $F$ in Hausdorff metric. This is not useful for my problem.

Thanks for your time.