Study of fractal image compression method with the purpose of improving compression quality


  • Zhurba A.O.



fractal, fractal compression, self-similarity, affine transformations, compression ratio, decompression.


The development of the Internet, along with the availability of increasingly powerful computers and other digital devices, cameras, scanners and printers, has led to the wide-spread use of digital images. In this regard, interest in improving data compression algo-rithms, such as images, is growing. Data compression is important for both transfer speed and storage efficiency. In addition to many commercial uses, compression technologies are also of interest in the military industry, such as applications for processing telemetry data from missile inter-ceptors or for archiving terrain image data for defense simulations. Solving the problem of image compression, or, more generally, image coding, has used advances and stimulated the development of many fields of engineering and math-ematics. The article examines fractal image compression — a data compression method based on the use of self-similar patterns in an image. This method allows you to achieve a high degree of compression while preserving image details. Fractal image compression is a unique and efficient approach to data compression based on the mathematical theory of fractals. Nowadays, it has important applications and advantages that make it a valuable tool in image processing. The main advantages include: 1. Preservation of details during compression. One of the key advantages of fractal compression is its ability to preserve a high degree of image detail in a relatively small amount of storage. This is especially important in situations where image quality must be preserved with limited storage and data transfer resources. 2. Efficiency of transmission through the network. Fractal compression allows for compact images, making it suitable for image transmission over a low-bandwidth network. This is especially true for mobile devices, the Internet of Things, and other scenarios where high bandwidth is not always available. 3. Adaptive compression for different resolutions. Fractal compression allows you to adapt the level of compression depending on the resolution and details of the image. This means that it can be used to compress various image sizes without significant loss of quality. 4. Data archiving and storage. Fractal compression can be useful for archiving and long-term storage of images, as it allows you to effectively reduce the amount of data without losing important information. This is especially important for libraries, archives, research databases and other data repositories. Fractal image compression remains a relevant and valuable tool in today's envi-ronment, thanks to its ability to efficiently compress, preserve details, and adapt to dif-ferent usage scenarios. Therefore, the study of its efficiency, the optimization of the soft-ware code to obtain a faster and better compression result, is an urgent task.


Mandelbrot, B.B. (1982) The Fractal Geometry of Nature. Freeman Press, New York.

Barnsley M. FractalsEverywhere / M. Barnsley. – London: AcademicPressInc., 1988. – 370 p.

Zhang Aihua, 2014. Fractal image coding combined with discretecosine transform complement. Computer Technology and Development, Vol. 24, No. 1, pp. 61– 68.

Vatolin, D. Data compression methods / D. Vatolin, A. Ratushnyak, M. Smirnov, V. Yukin. - M.: Dialog-MYFI, 2002. - 381 p.

Karpov, P. M. Fast fractal image compression algorithm [Text] / P. M. Karpov. – Scientific session of MYFI, 2006. – Vol. 15.

Shashin K.V., Zhurba A.O. Study of the fractal image coding method // Youth: sci-ence and innovation: materials of the 11th International scientific and technical conference of students, postgraduates and young scientists, Dnipro, November 22-24, 2023: in 2 volumes / National Technical University "Dnipro Polytechnic" – Dni-pro: NTU "DP", 2023. Volume 2. P. 12-13.