Fractal measures in nanoelectronics and neurodynamics

Abstract

The equation describing spatio-temporal evolution of additive physical quantities (measures) which depends on difference between fractal and topological dimensions of an object has been suggested. This equation is written in the form of two-dimensional map that takes into account a sign of derivative of measure. The notion for non-linear fractal measures with scale of measurement depending on the measure and external parameters has been proposed. Energy of excitonic formations and action potential of neurons have been considered as fractal measures. Results of the theory have been compared with experimental results