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Discontinuity, Nonlinearity, and Complexity 10(1) (2021) 135--142 | DOI:10.5890/DNC.2021.03.009

Marat Akhmet , Ejaily Milad Alejaily

Department of Mathematics, Middle East Technical University, 06800 Ankara, Turkey

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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 govern a relation between subsets of a metric space to build a porous self-similar structure. Examples are provided to confirm that the definition satisfies a large class of self-similar fractals. The new concepts create new frontiers for fractals and chaos investigations.

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