The deterministic fractals play an important role in computer graphics and mathematical sciences. The understanding of construction of such fractals, especially an ability of fractals construction from various types of polytopes is of crucial importance in several problems related both to the pure mathematical issues as well as some issues of theoretical physics. In the present paper the possibility of construction of fractals based on the Catalan solids is presented and discussed. The method and algorithm of construction of polyhedral strictly deterministic fractals is presented. It is shown that the fractals can be constructed only from a limited number of the Catalan solids due to the specific geometric properties of these solids. The contraction ratios and fractal dimensions are presented for existing fractals with adjacent contractions constructed based on the Catalan solids.

Following the "on condition maintenance" approach used for extending service life of an aircraft one of the major tasks is a nondestructive testing of its critical elements. Considering that many of elements of operated aircraft are manufactured from polymeric composites a special attention should be paid for diagnosing these elements due to their high vulnerability to barely visible impact damage. One of the primary testing techniques used for inspection of aircraft composite elements is an ultrasonic C-Scan technique which application results in planar images of emitted/received wave attenuation and a time of flight map. Due to the complex nature of barely visible impact damage occurrence it is difficult to analyze resulting C-Scan images. Therefore, using assistance based on image processing may help with "big–data" analysis of collected images. In this paper the authors proposed the image processing algorithm for semi-automatic evaluation of such damage distribution in aircraft composite structures. The algorithm is based on multilevel Otsu thresholding and morphological processing. Using the proposed algorithm an extraction of damage visualization from a C-Scan image as well as its characterization and 3D representation is possible. The developed approach will allow supporting diagnosing of composite structures with impact damage using C-Scan technique.