A class of continua that are not attractors of any IFS
  This paper presents a sufficient condition for a continuum in $R^n$ to be embeddable in $R^n$ in such a way that its image is not an attractor of any iterated function system. An example of a continuum in $R^2$ that is not an attractor of any weakly contracting iterated function system is also given. 
Marcin Kulczycki and Magdalena Nowak
math.DS