Peano continua with self regenerating fractals

We deal with the question of Masayoshi Hata: is every Peano continuum a topological fractal? A compact space $X$ fractal if there exists $\mathcal{F}$ finite family self-maps on such that $X=\bigcup_{f\in\mathcal{F}}f(X)$ and for open cover $\mathcal{U}$ $n\in\mathbb{N}$ all maps $f_1,\dots,f_n\in\mathcal{F}$ set $f_1\circ\dots\circ f_n(X)$ contained in some $U\in\mathcal{U}$. In paper we present idea how to extend show it contains so-called self regenerating nonempty interior. Hausdorff $A$ non-empty subset $U$, constant $A\setminus U$. The notion much better reflects intuitive perception self-similarity. classical fractals which are regenerating.