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THE NATURAL WORLD is filled with intricate detail . Consider the geometry on the back of your hand : the pores, the fine lines, and the color variations . A camera can capture that detail and, at your leisure, you can study the photo to see things you never noticed before . Can personal computers be made to carry out similar functions of image storage and analysis? If so, then image compression will certainly play a central role . The reason is that digitized imagesimages converted into bits for processing by a computer-demand large amounts of computer memory . For example, a highdetail gray-scale aerial photograph might be blown up to a 3'h-foot square and then resolved to 300 by 300 pixels per square inch with 8 significant bits per pixel . Digitization at this level requires 130 megabytes of computer memory-too much for personal computers to handle . For real-world images such as the aerialphoto, current compression techniques can achieve ratios ofbetween 2 to 1 and 10 to 1 . By these methods, our photo would still require between 65 and 13 megabytes . In this article, we describe some ofthe main ideas behind a new method for image compression using fractals . The method has yielded compression ratios in excess of 10,000 to 1 (bringing our aerial photo down to a manageable 13,000 bytes) . The color pictures in figures 1 through 5 were encoded using the new technique ; actual storage requirements for these images range from 100 to 2000 bytes . A mathematics research team at the Michael F. Barnsley andAlan D. Sloan