The circle as an attractor of an iterated function system on the plane

Abstract

We give an iterated function system (IFS) on the plane with the circle as attractor. In doing this, we also give a sufficient condition for radially contracting functions on the plane (or on Rn) to be a contraction. A counterexample shows that radial contractiveness is not enough to be a contraction. © 2006 Elsevier Inc. All rights reserved.