A lossy image compression technique based on splitting an image into parts that can each be represented by fractals. The representation of an image by a fractal consists of finding an image transformation that, when applied iteratively to any initial image at the decoder, produces a sequence of images that converges to a fractal approximation of the original. Essentially the encoding of the image is then an encoding of the transformation for each part of the image parts, and a description of the decomposition into parts. Fractal compression is computationally intensive. It has the ability to render images that appear lossless at one extreme and on the other hand the compressed images can be very small in size while still producing recognizable images.