Fractal-Cluster Theory and Its Applications for the Description of Biological Organisms

This article presents an overview of an alternative approach to the systematization and evolution of biological organisms on the basis of the fractal-cluster theory. It presents the foundations of the fractal-cluster theory for the self-organizing systems of the organism class. Static and dynamic efficiency criteria based on the fractal-cluster relations and the analytical apparatus of nonequilibrium thermodynamics are presented. We introduce a highly sensitive static criterion, D, which determines the deviation in the value of the clusters and subclusters of the fractal-cluster system structures from their reference values. Other static criteria are the fractal-cluster entropy H and the free energy F of an organism. The dynamic criterion is based on Prigogine's theorem and is determined by the second differential of the temporal trend of the fractal-cluster entropy H. By using simulations of the cluster variations for biological organisms in the (H, D, F)-space, the criteria for the fractal-cluster stochastics as well as for energy and evolution laws are obtained. The relationship between the traditional and fractal-cluster approaches for identifying an organism is discussed.

Automated summary

This article presents an alternative approach to the systematization and evolution of biological organisms based on the fractal-cluster theory. It introduces the foundations of the fractal-cluster theory in the self-organizing systems of organisms, and presents static and dynamic efficiency criteria. By using simulations of cluster variations, criteria for fractal-cluster stochastics, energy, and evolution laws are obtained.