Discontinuity, Nonlinearity, and Complexity


AKHMET M., Alejaily E. M.

Discontinuity, Nonlinearity, and Complexity, vol.10, no.1, pp.135-142, 2021 (Peer-Reviewed Journal) identifier

  • Publication Type: Article / Article
  • Volume: 10 Issue: 1
  • Publication Date: 2021
  • Doi Number: 10.5890/dnc.2021.03.009
  • Journal Name: Discontinuity, Nonlinearity, and Complexity
  • Journal Indexes: Scopus
  • Page Numbers: pp.135-142
  • Keywords: Abstract fractals, Abstract self-similarity, Chaos, Self-similar fractals

Abstract

© 2021 L&H Scientific Publishing, LLC. All rights reserved.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.