Generalized Countable Iterated Function Systems

Nicolae Adrian Secelean

One of the most common and most general way to generate fractals is by using iterated function systems which consists of a 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.