Linear Fractals with Weights

Linear fractals associated with weights are investigated. Such fractals are important from a conservation law perspective that is relevant in a variety of physical systems such as materials science, sand dune fractals, barred galaxies, as well as in temporal processes like in the electroencephalogra...

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Bibliographic Details
Published inParallel processing letters Vol. 33; no. 4
Main Author Kak, Subhash
Format Journal Article
LanguageEnglish
Published Singapore World Scientific Publishing Company 01.12.2023
World Scientific Publishing Co. Pte., Ltd
Subjects
Algorithms
Barred galaxies
Biological activity
Conservation laws
Fractal transforms
Fractals
Information theory
Fractals
noninteger dimensionality
system evolution
indistinguishability
linear fractals
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ISSN0129-6264
1793-642X
DOI10.1142/S012962642340011X

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Summary:Linear fractals associated with weights are investigated. Such fractals are important from a conservation law perspective that is relevant in a variety of physical systems such as materials science, sand dune fractals, barred galaxies, as well as in temporal processes like in the electroencephalogram (EEG). The weight associated with fractals is an additional feature that may be associated with distributions consistent with the ubiquitous power law and the first digit phenomenon. These distributions form a bridge to processes and applications in natural, biological, and engineering systems and, therefore, open up the possibility of the application of linear weighted fractals to these subjects. Two linear fractal algorithms that are near optimal in the information theoretic sense are described. A mechanism for the emergence of these fractals is proposed: it is the indistinguishability amongst the particles in the evolution and transformation of physical systems. Since the fractal approach is an established method of signal processing and coding, the newly proposed weighted fractals have the potential to lead to new useful algorithms.
Bibliography:This article is part of the “Special Issue on Novel Computational Approaches to the Universe”, edited by Andrew Schumann and Jerzy Król (University of Information Technology and Management in Rzeszow, Poland).
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ISSN:0129-6264
1793-642X
DOI:10.1142/S012962642340011X