  With any self-similar action of a finitely generated group $G$ of
automorphisms of a regular rooted tree $T$ can be naturally associated an
infinite sequence of finite graphs $\{\Gamma_n\}_{n\geq 1}$, where $\Gamma_n$
is the Schreier graph of the action of $G$ on the $n$-th level of $T$.
Moreover, the action of $G$ on $\partial T$ gives rise to orbital Schreier
graphs $\Gamma_{\xi}$, $\xi\in \partial T$. Denoting by $\xi_n$ the prefix of
length $n$ of the infinite ray $\xi$, the rooted graph $(\Gamma_{\xi},\xi)$ is
then the limit of the sequence of finite rooted graphs
$\{(\Gamma_n,\xi_n)\}_{n\geq 1}$ in the sense of pointed Gromov-Hausdorff
convergence. In this paper, we give a complete classification (up to
isomorphism) of the limit graphs $(\Gamma_{\xi},\xi)$ associated with the
Basilica group acting on the binary tree, in terms of the infinite binary
sequence $\xi$.
