Detail publikace

Entropy of fractal systems

ZMEŠKAL, O. DZIK, P. VESELÝ, M.

Originální název

Entropy of fractal systems

Anglický název

Entropy of fractal systems

Jazyk

en

Originální abstrakt

The Kolmogorov entropy is an important measure which describes the degree of chaoticity of systems. It gives the average rate of information loss about a position of the phase point on the attractor. Numerically, the Kolmogorov entropy can be estimated as the Rényi entropy. A special case of Rényi entropy is the information theory of Shannon entropy. The product of Shannon entropy and Boltzmann constant is the thermodynamic entropy. Fractal structures are characterized by their fractal dimension. There exists an infinite family of fractal dimensions. A generalized fractal dimension can be defined in an E-dimensional space. The Rényi entropy and generalized fractal dimension are connected by known relation. The calculations of fractal dimensions and entropies for different orders q will be demonstrated with the help of HarFA software application (Harmonic and Fractal image Analyzer), that was developed by one of the authors of this contribution. This software can be used for image analysis as well as for educative purposes.

Anglický abstrakt

The Kolmogorov entropy is an important measure which describes the degree of chaoticity of systems. It gives the average rate of information loss about a position of the phase point on the attractor. Numerically, the Kolmogorov entropy can be estimated as the Rényi entropy. A special case of Rényi entropy is the information theory of Shannon entropy. The product of Shannon entropy and Boltzmann constant is the thermodynamic entropy. Fractal structures are characterized by their fractal dimension. There exists an infinite family of fractal dimensions. A generalized fractal dimension can be defined in an E-dimensional space. The Rényi entropy and generalized fractal dimension are connected by known relation. The calculations of fractal dimensions and entropies for different orders q will be demonstrated with the help of HarFA software application (Harmonic and Fractal image Analyzer), that was developed by one of the authors of this contribution. This software can be used for image analysis as well as for educative purposes.

Dokumenty

BibTex


@article{BUT99164,
  author="Oldřich {Zmeškal} and Petr {Dzik} and Michal {Veselý}",
  title="Entropy of fractal systems",
  annote="The Kolmogorov entropy is an important measure which describes the degree of
chaoticity of systems. It gives the average rate of information loss about a position
of the phase point on the attractor. Numerically, the Kolmogorov entropy can be
estimated as the Rényi entropy. A special case of Rényi entropy is the information
theory of Shannon entropy. The product of Shannon entropy and Boltzmann constant
is the thermodynamic entropy.
Fractal structures are characterized by their fractal dimension. There exists an infinite
family of fractal dimensions. A generalized fractal dimension can be defined
in an E-dimensional space. The Rényi entropy and generalized fractal dimension
are connected by known relation.
The calculations of fractal dimensions and entropies for different orders q will be demonstrated with the help of HarFA
software application (Harmonic and Fractal image Analyzer), that was developed by one of the authors of this contribution.
This software can be used for image analysis as well as for educative purposes.",
  address="Elsevier",
  chapter="99164",
  doi="10.1016/j.camwa.2013.01.017",
  howpublished="print",
  institution="Elsevier",
  number="2",
  volume="65",
  year="2013",
  month="january",
  pages="136--146",
  publisher="Elsevier",
  type="journal article - other"
}