Fractal image compression currently relies on the partitioning of an image into both
coarse "domain" segments and fine "range" segments, and for each range element, determines the domain element that best transforms into the range element. Under normal circumstances, this algorithm produces a structure equivalent to a recurrent iterated function system. This equivalence allows recent innovations to fractal image compression to be applied to the general inverse problem of recurrent iterated function systems. Additionally, the RIFS representation encodes bitmaps (bi-level images) better than current fractal image compression techniques.