The iterated function system constituted by a collection of maps f_i is said to satisfy the Open Set Condition (OSC) if there exists an open set V such that f_i(V) is a subset of V for each i, and the f_i(V) are pairwise disjoint.

This property is rather strong and implies in particular that the Hausdorff dimension of the invariant set is equal to its similarity dimension.

For more detail see [1].

References:

[1] K. Falconer, Fractal Geometry, 1990.