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arXiv.org e-Print Archive
Preprint . 2019
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zbMATH Open
Article . 2021
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The interdisciplinary journal of Discontinuity Nonlinearity and Complexity
Article . 2021 . Peer-reviewed
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https://dx.doi.org/10.48550/ar...
Article . 2019
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Abstract Fractals

Abstract fractals
descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Mar 2021Embargo end date: 01 Jan 2019Publisher:L and H Scientific Publishing, LLCJournal:The interdisciplinary journal of Discontinuity, Nonlinearity, and Complexity, volume 10, pages 135-142 (issn: 2164-6376, eissn: 2164-6414, Copyright policy )
Authors: Akhmet, Marat; Alejaily, Ejaily Milad;

doi: 10.5890/dnc.2021.03.009 , 10.48550/arxiv.1908.04273

arXiv: 1908.04273

Abstract Fractals

Abstract

We develop a new definition of fractals which can be considered as an abstraction of the fractals determined through self-similarity. The definition is formulated through imposing conditions which are governed the relation between the subsets of a metric space to build a porous self-similar structure. Examples are provided to confirm that the definition is satisfied by large class of self-similar fractals. The new concepts create new frontiers for fractals and chaos investigations.

Keywords

Fractals, Mathematics - Metric Geometry, FOS: Mathematics, Metric Geometry (math.MG)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green