Detail publikace

Entropy of fractal systems

ZMEŠKAL, O. DZIK, P. VESELÝ, M.

Originální název

Typ

článek v časopise - ostatní, Jost

Jazyk

angličtina

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.

Klíčová slova

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

Autoři

ZMEŠKAL, O.; DZIK, P.; VESELÝ, M.

Rok RIV

2013

Vydáno

1. 1. 2013

Nakladatel

Elsevier

Místo

Amsterdam, Holland

ISSN

0898-1221

Periodikum

Computers and Mathematics with Applications

Ročník

Číslo

Stát

Spojené království Velké Británie a Severního Irska

Strany od

136

Strany do

146

Strany počet

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"
}