introduced an image compression scheme using fractal interpolation surfaces which are attractors of some RIFSs. A hexagonal structure called the Spiral Architecture (SA) was proposed by Sheridan in 1996. Fisher improved the partition of Jacquin. RIFSs which have been used in image compression schemes consist of transformations which have a constant vertical contraction factor. Jacquin presented a more flexible method of FIC than Barnsley’s, which is based on recurrent iterated function systems (RIFSs) introduced first by him. So in FIC iterated function systems are used for modeling. FIC is based on the idea that any image contains self-similarities, that is, it consists of small parts similar to itself or to some big part in it. They introduce in another work a better way to compress images, and after that, (FIC) has been widely studied by many scientists. Fractal image compression (FIC) was introduced by Barnsley and Sloan. Finally, in 1975 Mandelbrot coined the word fractal to denote an object whose Hausdorff-Besicovitch dimension is greater than its topological dimension. In the 1960s, Benot Mandelbrot started investigating self-similarity in papers such as How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension, which built on earlier work by Lewis Fry Richardson. However, without the aid of modern computer graphics, they lacked the means to visualize the beauty of many of the objects that they had discovered. Iterated functions in the complex plane were investigated in the late 19th and early 20th centuries by Henri Poincar, Felix Klein, Pierre Fatou and Gaston Julia. The mathematics behind fractals began to take shape in the 17th century when mathematician and philosopher Leibniz considered recursive self-similarity (although he made the mistake of thinking that only the straight line was self-similar in this sense). Finally, the comparison between filtered ranges method and self-organizing Results are presented and the performance of the proposed algorithm isĭiscussed. The neural network algorithms haveīeen applied on the process of compression (encryption). The image that have a specific milestone. To reduce the time required for image compression by excluding some parts of Image space, which deals with the computer. Mathematical formulation form is also provided on the digital Then this idea is applied by iterated function system, iterative systemįunctions and grayscale iterated function system down to general Which is the cornerstone of the mathematical idea of fractal image compression. This inverse problem is based on collage theorem In this paper, the idea of the inverse problem ofįixed point is introduced. The process of image compression (encoding) and conversion into a system of Of the main disadvantages of fractal image data compression is a loss time in