Summary: One of the most common and most general ways to generate fractals apply iterated function systems consisting of finite or infinitely many maps. Generalized countable iterated function systems (GCIFS) are a generalization of countable iterated function systems by considering contractions from \(X\times X\) into \(X\) instead of contractions on the metric space \(X\) to itself, where \((X,d)\) is a compact metric space. If all contractions of a GCIFS are Lipschitz with respect to a parameter and the supremum of the Lipschitz constants is finite, then the associated attractor depends continuously on the respective parameter.