We consider the attractor T of injective contractions f[sub 1], ... , f[sub m] on R[sup 2] which satisfy the Open Set Condition. If T is connected, then T's interior T° is either empty or has no holes, and T's boundary ∂T is connected; if further T° is non-empty and connected, then ∂T is a simple closed curve, thus T is homeomorphic to the unit disk {x ε R[sup 2]: |x| ≤ 1}.