Publication detail

Entropy of fractal systems

ZMEŠKAL, O. DZIK, P. VESELÝ, M.

Original Title

Type

journal article - other

Language

English

Original Abstract

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.

Keywords

Fractal physics, Fractal geometry, Fractal dimension, Fractal measure, Kolmogorov entropy, Rényi entropy,m Shannon entropy, Thermodynamic entropy

Authors

ZMEŠKAL, O.; DZIK, P.; VESELÝ, M.

RIV year

2013

Released

1. 1. 2013

Publisher

Elsevier

Location

Amsterdam, Holland

ISBN

0898-1221

Periodical

Computers and Mathematics with Applications

Year of study

Number

State

United Kingdom of Great Britain and Northern Ireland

Pages from

136

Pages to

146

Pages count

BibTex

@article{BUT99164,
  author="Oldřich {Zmeškal} and Petr {Dzik} and Michal {Veselý}",
  title="Entropy of fractal systems",
  journal="Computers and Mathematics with Applications",
  year="2013",
  volume="65",
  number="2",
  pages="136--146",
  doi="10.1016/j.camwa.2013.01.017",
  issn="0898-1221"
}