  We consider a quasi-linear homogenization problem in a two-dimensional
pre-fractal domain $\Omega_n$, for $n\in\mathbb{N}$, surrounded by thick fibers
of amplitude $\varepsilon$. We introduce a sequence of "pre-homogenized" energy
functionals and we prove that this sequence converges in a suitable sense to a
quasi-linear fractal energy functional involving a $p$-energy on the fractal
boundary. We prove existence and uniqueness results for (quasi-linear)
pre-homogenized and homogenized fractal problems. The convergence of the
solutions is also investigated.
