**5. Conclusions**

Since the time of the ancient Greeks, space and chaos have been considered oppositions in the concept of beauty. Beauty is determined by the interaction, the harmonic balance of these two oppositions. Symmetry embodies the cosmos, which reveals in beauty a stable order, and fractality penetrates into the second opposition, which reflects in beauty the result of the self-organization of the chaos of nature or the freedom of human thought. Thus, symmetry and fractality are two sides of beauty, aesthetically complementing each other. The synergetic worldview opens to humanity a new vision of beauty—beauty as a synthesis of symmetry and fractality, the most important components of the scientific picture of the world. The interrelated study of symmetry and fractal geometry contributes both to the increase of interest in the study of mathematics and aesthetic education.
