Approximating the Attractor Set of Countable Iterated Function Systems by $$\alpha $$ α -Dense Curves

Abstract

We present a new procedure to approximate, with arbitrarily small and controlled error, the attractor set of a countable iterated function system. Such procedure can be applied to iterated function systems. A key tool here is the \(\alpha \)-dense curves which are, from the Hausdorff metric point of view, a generalization of the space-filling curves.