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This paper presents a fast, new image-based technique for determining the connectedness of iterated function system attractors. It explores the use of a iterated function system (IFS) as a geometric representation for shape interpolation. For each shape interpolation, a two parameter family of iterated function system is defined, and a connectedness locus for these shapes is plotted, in order to maintain connectedness during the interpolation. The algorithm generates a smooth continuous shape transformation sequence from two given IFS attractors, initial and final, using polar decomposition . Polar decomposition is used for interpolation because its factors are unique, coordinate independent, simple and efficient to compute, and have physical and visual interpretation which are not found in other decomposition methods. Moreover, we apply it for natural image animation because it extracts the individual transformation components from a general affine transformation matrix and provides a basis for more controlled shape interpolation.