Synthesis of fractal images in the problems of compression of static and dynamic UHD images

In recent years, geometric models have been used to describe natural objects with combinations of simple shapes such as lines, triangles, circles, spheres and polyhedra. However, more complex natural objects such as cellular material, cloud formations and tree canopies are difficult to describe using these familiar sets of shapes. Fortunately, advances in computing tools have made it possible to take mathematics to a higher level, leading to the discovery of unique and different models. In particular, fractals have helped us understand natural phenomena and processes. This paper presents the results of a modified genetic algorithm for fractal coding applied to still images and video sequences. The relationship between compression coefficients and sequence block size is studied and fractal compression is compared with the standard MPEG-4 HEVC compression algorithm. The results show that fractal compression can achieve twice the compression factor with the same signal-to-noise ratio. It is becoming increasingly clear that the boundary between mathematics and information is blurring and the study of such expressions can lead to the discovery of new and unique models.