Fractal image compression is a technique that uses fractals to represent images with fewer bits of data than the original. This method associates a fractal with an image, allowing for high compression ratios. The fractal can be described with a few succinct rules, which require less data than the image itself. The technique supports both lossless and lossy compression, and is stable in that small errors in codes lead to small errors in image data. It has applications in NASA missions and is supported by various research institutions. The technique involves an iterated function system (IFS), which consists of affine transformations and probabilities. Affine transformations are used to describe the fractal and are defined by six coefficients. The probabilities form a linkage matrix used in the decoding process. The Hausdorff distance is used to measure the similarity between images and is crucial for the collage theorem, which allows for the control of the fidelity of the encoded image. The collage theorem states that if the Hausdorff distance between a target image and the image generated by an IFS code is small, then the Hausdorff distance between the target image and the attractor of the code is even smaller. This theorem is used to find the IFS code for an image by arranging small deformed copies of the target image to cover it as closely as possible. Fractal image compression has been applied to various data types, including color and grey-scale images. It has been used in NASA missions for data compression and transmission, and has potential applications in scientific data analysis and management. The technique is efficient for animation and can provide interactive browsing of data on existing networks. It is also useful for data storage and transmission, especially in environments with bandwidth bottlenecks. Fractal image compression can retain certain recognizable features of an image even after high compression, making it valuable for scientific applications. The technique is supported by various research institutions and has been demonstrated in hardware implementations.Fractal image compression is a technique that uses fractals to represent images with fewer bits of data than the original. This method associates a fractal with an image, allowing for high compression ratios. The fractal can be described with a few succinct rules, which require less data than the image itself. The technique supports both lossless and lossy compression, and is stable in that small errors in codes lead to small errors in image data. It has applications in NASA missions and is supported by various research institutions. The technique involves an iterated function system (IFS), which consists of affine transformations and probabilities. Affine transformations are used to describe the fractal and are defined by six coefficients. The probabilities form a linkage matrix used in the decoding process. The Hausdorff distance is used to measure the similarity between images and is crucial for the collage theorem, which allows for the control of the fidelity of the encoded image. The collage theorem states that if the Hausdorff distance between a target image and the image generated by an IFS code is small, then the Hausdorff distance between the target image and the attractor of the code is even smaller. This theorem is used to find the IFS code for an image by arranging small deformed copies of the target image to cover it as closely as possible. Fractal image compression has been applied to various data types, including color and grey-scale images. It has been used in NASA missions for data compression and transmission, and has potential applications in scientific data analysis and management. The technique is efficient for animation and can provide interactive browsing of data on existing networks. It is also useful for data storage and transmission, especially in environments with bandwidth bottlenecks. Fractal image compression can retain certain recognizable features of an image even after high compression, making it valuable for scientific applications. The technique is supported by various research institutions and has been demonstrated in hardware implementations.