New Methods for Estimating the Dimension Fractal Introducing the Artificial Intelligence

Methods provided actually for estimating the fractal dimension (especially methods of Richardson, Minkowski, Weibel and Flook) differ only by the way which is how to recover the fractal subject previously studied. The concept of optimal recovery is not found by these methods but in fact, the more we...

Full description

Saved in:
Bibliographic Details
Published inActa applicandae mathematicae Vol. 109; no. 3; pp. 1043 - 1051
Main Authors Zerroug, A., Schoëvaërt-Brossault, D., Rebiai, S.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.03.2010
Springer Nature B.V
Subjects
Algorithms
Applications of Mathematics
Artificial intelligence
Calculus of Variations and Optimal Control; Optimization
Computational Mathematics and Numerical Analysis
Fractals
Markov analysis
Mathematical analysis
Mathematics
Mathematics and Statistics
Methods
Partial Differential Equations
Probability Theory and Stochastic Processes
Simulation
Studies
Markov fields
Fractal dimension
Adjustment tests
Stereological simulation
Online AccessGet full text

Cover

More Information
Summary:Methods provided actually for estimating the fractal dimension (especially methods of Richardson, Minkowski, Weibel and Flook) differ only by the way which is how to recover the fractal subject previously studied. The concept of optimal recovery is not found by these methods but in fact, the more we minimize this tool the more it gets close to the theoretical dimension. Therefore, we develop a new concept which incorporates artificial intelligence, consequentially the concept of optimality is put forward.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0167-8019
1572-9036
DOI:10.1007/s10440-008-9358-4