SELF-SIMILARITY COEFFICIENTS OF DYNAMIC PROCESSES IN NATURAL MEDIA

Abstract

We know that self-similarity and a hierarchical organization are typical of the structure of complex natural dynamic systems. In the course of an empirical analysis of dynamic processes in liquid, solid and gaseous natural media we found that the ratio of the scales of the typical dimensions of a deformable medium before and after deformation (i.e., the self-similarity coefficient k) has a rather small range of variation, from 2 to 6. The simplest case, which we can use to demonstrate self-similarity, is vortex formation in a flow of liquid or gas incident on some barrier, for example, a system of coherent vortices in the cloud field forming behind Jan Mayen Island by an incidental air flow. The hierarchy of dimensions of celestical bodies and the distribution of mass in the universe, the hierarchy of scales of biological structures (plant and animal organisms, communities of organisms), and even social structures, also exhibit changes in hierarchical coefficients in the range between 2 and 6. We thus suggest that the coefficient is universal to self-organization processes in natural media. A consequence of its universality is that abiotic hierarchical systems have fifth-order symmetry axes which are indissolubly connected with the so-called 'golden section' rule, which is important in the morphology of life forms.