Informational and entropic criteria of self-similarity of fractals and chaotic signals

Abstract

 Abstract. Information entropy and fractal dimension of a set of physical values are usually used us quantitative characteristic of chaos. Normalization of entropy is a well-known problem. This work is devoted to develop a method to do this. In the work proposed criteria for self-similarity of information and informational entropy. We have defined normalized values of information (I1 = 0.567) and informational entropy (I2 = 0.806) as fixed points of probability density function of information and informational entropy. Meaning of these values is described as criteria of self-similarity of fractals and chaotic signals with different dimensions. We have shown that self-similarity occurs if normalized informational entropy S belongs to the ranges [0,I1), [I1,I2), [I2,1), that corresponds to topological dimensions from 1 to 3 of quasi-periodic, chaotic, stochastic objects. Validity of these findings has been confirmed by calculation of entropy for hierarchical sets of well-known fractals and nonlinear maps. These criteria can be applied to a wide range of problems, where entropy is used.

      G M T   Английский Испанский Итальянский Казахский Китайский Трад Китайский Упр Корейский Русский Турецкий Французский   Английский Испанский Итальянский Казахский Китайский Трад Китайский Упр Корейский Русский Турецкий Французский                 Звуковая функция ограничена 200 символами     Настройки : История : Обратная связь : Donate Закрыть