Fractal Image Compression is a technique that associates a fractal with an image, allowing for high compression ratios while retaining significant image information. The fractal is described by a few concise rules, which are encoded using fewer bits than the original image, leading to compression. This method supports both lossless and lossy modes, with the latter achieving higher compression ratios. The technique is computationally intensive but can be implemented efficiently due to the nature of the transformations involved. The Collage Theorem provides a solution to the inverse problem of finding the rules that encode an image as a fractal, enabling high-resolution, color images to be encoded in a few thousand bytes. The technique is supported by basic research at Georgia Tech and other universities, funded by organizations like DARPA, AFOSR, NSF, and ONR. Commercial applications are being explored, with Iterated Systems, Inc. formed to commercialize the technology. The compression process involves an iterated function system (IFS) composed of affine transformations and probabilities. The Hausdorff distance is used to measure the fidelity of the encoded image, ensuring that small errors in the code lead to small errors in the image. The decoder uses these transformations to reconstruct the original image, and the attractor of the IFS code is the encoded image. NASA applications highlight the technique's utility in space missions, particularly in data quality, scientific utility, and data management. Fractal image compression can significantly reduce data volume, improve data transmission, and enhance interactive access to scientific data. It also retains geometric and measure-theoretic information, making it useful for texture and object identification and classification.Fractal Image Compression is a technique that associates a fractal with an image, allowing for high compression ratios while retaining significant image information. The fractal is described by a few concise rules, which are encoded using fewer bits than the original image, leading to compression. This method supports both lossless and lossy modes, with the latter achieving higher compression ratios. The technique is computationally intensive but can be implemented efficiently due to the nature of the transformations involved. The Collage Theorem provides a solution to the inverse problem of finding the rules that encode an image as a fractal, enabling high-resolution, color images to be encoded in a few thousand bytes. The technique is supported by basic research at Georgia Tech and other universities, funded by organizations like DARPA, AFOSR, NSF, and ONR. Commercial applications are being explored, with Iterated Systems, Inc. formed to commercialize the technology. The compression process involves an iterated function system (IFS) composed of affine transformations and probabilities. The Hausdorff distance is used to measure the fidelity of the encoded image, ensuring that small errors in the code lead to small errors in the image. The decoder uses these transformations to reconstruct the original image, and the attractor of the IFS code is the encoded image. NASA applications highlight the technique's utility in space missions, particularly in data quality, scientific utility, and data management. Fractal image compression can significantly reduce data volume, improve data transmission, and enhance interactive access to scientific data. It also retains geometric and measure-theoretic information, making it useful for texture and object identification and classification.