Applications of image compression have been gaining importance over the years in medical fields. The medical imaging modalities produced a large amount of information on all levels of hospital care. This information, in the form of images, needs to be stored for future references. While compressing the medical images, it is necessary to maintain high diagnostic quality with a high compression rate. Several image compression approaches have been developed towards the direction of the storage space problem in such a way that the doctors accurately and reliably diagnose the patient’s diseases from the reconstructed image after decompression. A high compression ratio is required to reduce the storage space due to the large size of medical images. Fractal image compression is a lossy technique to compress the image in a coded form instead of pixels and is differentiated by its long encoding time with a high compression ratio, resolution-independent, fast decoding, and self-similarity. The main purpose of this paper is to present a comparative performance study of the three coding schemes of fractal compression for grayscale medical images based on fixed partition. The first two coding schemes are based on the pixel-pattern measure and the third scheme is a proposed method based on the fractal dimension for complexity measure of range and domain blocks. The comparative study included encoding time, peak signal to noise ratio, and compression ratio, as a result, has been accomplished.