Some Natural Phenomena and Sign Combinatorial Spaces

Abstract

The literature describes many natural phenomena associated with combinatorial numbers including golden number that is represented by Fibonacci numbers. This suggests that the laws of combinatorics are inherent in nature. To explain such natural phenomena as the presence of combinatorial numbers in nature, the formation of fractal structures and symmetry in biology one applies the properties of sign combinatorial spaces. 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, these sets are characterized by the 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 is combinatorial configurations of different types exist in two states: convolved (rest) and developed (dynamics). Axioms are introduced for them. As in combinatorial sets, fractals and symmetries of different kinds are formed in the process of these spaces unfolding. The axioms of sign combinatorial spaces are valid for some natural ones including the biological. Therefore studying symmetry and fractals in combinatorics we can explain how they are formed in biology. The question of how the symmetry arises in developed biological spaces has not been answered yet. Knowing the symmetry formation in combinatorial sets, one can explain the symmetry formation in biology.