Interpolation of two-dimensional shapes described by iterated function systems is explored. Iterated function systems define shapes using self-transformations, and interpolation of these shapes requires interpolation of these transformations. Polar decomposition is used to avoid singular intermediate transformations and to better simulate articulated motion. Unlike some other representations, such as polygons, shaped described by iterated function systems can become totally disconnected. A new, fast and image-based technique for determining the connectedness of an iterated function system attractor is introduced. For each shape interpolation, a two parameter family of iterated function systems is defined, and a connectedness locus for these shapes is plotted, to maintain connectedness during the interpolation.