ДЕЯКІ ПРИРОДНІ ЯВИЩА ТА ЗНАКОВІ КОМБІНАТОРНІ ПРОСТОРИ

• Datum: 2020
• 1. Verfasser: Tymofijeva, N.К.
• Format: Artikel
• Sprache: English
• Veröffentlicht: V.M. Glushkov Institute of Cybernetics of NAS of Ukraine 2020
• Schlagworte: комбінаторні числа; знакові комбінаторні простори; симетрія комбінаторних множин; симетрія комбінаторних конфігурацій; фрактали
• Online Zugang: https://jais.net.ua/index.php/files/article/view/465
• Назва журналу: Problems of Control and Informatics

The literature describes many natural phenomena associated with combinatorial numbers, including the «gold» number that is represented by Fibonacci numbers. This suggests that the laws of combinatorics are inherent in nature. To explain such natural phenomenons as the presence of combinatorial numbers in nature, the formation of fractal structures and symmetry in biology, the properties of sign combinatorial spaces are used. In the combinatorial sets ordered by certain rules the numerical sequences that specify in them the number of combinatorial configurations also contain combinatorial numbers, including Fibonacci numbers. In addition, they are characterized by symmetry. In these sets, symmetry is modeled by a finite sequence of numbers that define the number of combinatorial configurations in subsets. Their values increase to the largest and then decrease (or decrease to the smallest and then increase). The symmetry plane passing through the largest (or smallest) number of the sequence divides it into two parts whose values from the center decrease (or increase) evenly, but these parts are not necessarily mirror symmetrical. They are characterized by both approximate and exact symmetry. Sign combinatorial spaces, the point of which are combinatorial configurations of different types, exist in two states: convolute (tranquility) and deployed (dynamics). Axioms are introduced for them. As in combinatorial sets, fractals and symmetries of different kinds are formed in the process of unfolding these spaces. The axioms of sign combinatorial spaces hold for some natural ones, including biological. Therefore, exploring symmetry and fractals in the combinatorics, we can explain how they are formed in biology. The question of how it arises symmetry in deployed biological spaces is not yet found. Knowing the formation of symmetry in combinatorial sets, one can explain the formation of symmetry in biology.