Abstract: Our presentation starts with a brief introduction to Hutchinson-Barnsley fractals and their usefulness in image compression. We proceed to introduce a novel method for determining a finite family of closed balls that encompass a specified Hutchinson-Barnsley fractal, also known as the attractor of an iterated function system. Our approach draws inspiration from D. Canright's method outlined in "Estimating the spatial extent of attractors of iterated function systems", Comput. & Graphics, 18 (1994), 231-238. However, we simplify Canright's system for determining the radii of the balls. Specifically, while Canright algorithmically finds a solution of his system, we are able to determine the algebraic expression of a solution for our system. A by-product of our method is the ability to find a cover of the attractor using a finite family of closed balls with radii smaller than a prescribed value, albeit at the cost of increasing the number of elements in the family. Finally, we suggest future research directions for adapting our method to various generalizations of Hutchinson-Barnsley fractals.