The shark teeth is a topological IFS-attractor

We show that the space called the shark teeth is a topological IFS-attractor, that is, for every open cover of $X=\bigcup^n_{i=1}f_i(X)$ , its image under every suitable large composition from the family of continuous functions $\{f_1,\dots,f_n\}$ lies in some set from the cover. In particular, there exists a space that is not homeomorphic to any IFS-attractor but is a topological IFS-attractor.