Fractal images defined by an iterated function system (IFS) are specified by a finite number of contractive affine transformations. In order to plot the attractor of an IFS on the screen of a digital computer, it is necessary to determine a bounding area for the attractor. Given a point on the plane, we obtain a formula for the radius of a circle centred on that point that contains the attractor of the IFS. We then describe an algorithm to find the point on the plane such that the bounding circle centred on that point has minimum radius. (C) 1997 Elsevier Science B.V.