Entropy of fractal systems

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26310%2F13%3APU103311" target="_blank" >RIV/00216305:26310/13:PU103311 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.camwa.2013.01.017" target="_blank" >http://dx.doi.org/10.1016/j.camwa.2013.01.017</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.camwa.2013.01.017" target="_blank" >10.1016/j.camwa.2013.01.017</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Entropy of fractal systems

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Entropy of fractal systems

Popis výsledku anglicky

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.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

CF - Fyzikální chemie a teoretická chemie

OECD FORD obor

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Projekt

<a href="/cs/project/FR-TI1%2F144" target="_blank" >FR-TI1/144: *Multikomponentní elektronické systémy na bázi organických sloučenin</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2013

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Computers and Mathematics with Applications

ISSN

0898-1221

e-ISSN

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Svazek periodika

65

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

12

Strana od-do

136-146

Kód UT WoS článku

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EID výsledku v databázi Scopus

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