  Given an integer $n\geq 2$ and a digit set ${\mathcal D}\subsetneq
{0,1,...,n-1}^2$, there is a self-similar set $F \subset {\Bbb R}^2$ satisfying
the set equation: $F=(F+{\mathcal D})/n$. We call such $F$ a fractal square. By
studying a periodic extension $H= F+ {\mathbb Z}^2$, we classify $F$ into three
types according to their topological properties. We also provide some simple
criteria for such classification.
