  Quantum systems with short range interactions are known to respect an area
law for the entanglement entropy: the von Neumann entropy $S$ associated to a
bipartition scales with the boundary $p$ between the two parts. Here we study
the case in which the boundary is a fractal. We consider the topologically
ordered phase of the toric code with a magnetic field. When the field vanishes
it is possible to analytically compute the entanglement entropy for both
regular and fractal bipartitions $(A,B)$ of the system, and this yields an
upper bound for the entire topological phase. When the $A$-$B$ boundary is
regular we have $S/p =1$ for large $p$. When the boundary is a fractal of
Hausdorff dimension $D$, we show that the entanglement between the two parts
scales as $S/p=\gamma\leq1/D$, and $\gamma$ depends on the fractal considered.
