MODELING OF NATURAL SPACES USING COMBINATORICS

Abstract

Phenomena associated with combinatorial numbers, in particular Fibonacci numbers, are observed in nature. These numbers are manifested during the formation of the inflorescence of some flowers, the scales of cones, the placement of the leaves of trees and other plants. The arms of the galaxies, the spiral of rose petals that have blossomed, form a logarithmic spiral. Modeling natural spaces using combinatorics, in particular sign combinatorial spaces, makes it possible to explain the presence of combinatorial numbers in nature. These spaces are formed due to the generation of combinatorial configurations from the elements of the basic set according to certain rules. If you count the number of these configurations in the combinatorial set and form finite sequences from their values, then the latter form an arithmetic triangle through which the Fibonacci numbers appear. The values of these sequences, which are geometrically presented through polar coordinates, form logarithmic spirals. The ordering of combinatorial sets can be both chaotic and carried out according to strict rules. Similar to the generation of combinatorial sets, sign combinatorial spaces are constructed, the points of which are combinatorial configurations. They exist in two states: collapsed (at rest) and unfolded (dynamics). Collapsed is given by a sign that contains all the properties of expanded spaces. It is given by the base set, (one or several), its type and the rules of deployment from the elements of the base set of points of the deployed space. Sign combinatorial spaces have the property of convolve. The combinatorial spaces described in the literature are deployed sign spaces. We observe the same in living nature. Consider a seed or a cell as a collapsed biological space, which will be defined by an information sign. Under the action of certain factors (for plants, it is heat, moisture and earth), a living object is formed – an deployed space, which has the possibility to convolve from biological spaces of various types. The speech space is formed from the elements of the speech tract that form the basic set. That is, the specified spaces are characterized by the axioms of sign combinatorial spaces, which also exist in rest and dynamics. The point of these spaces are such combinatorial configurations as samples of different types. Similarly, other natural spaces can be submitted: informational, physical, etc.