ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

A Survey on Self Similarity

Discontinuity, Nonlinearity, and Complexity 11(3) (2022) 409--424 | DOI:10.5890/DNC.2022.09.005

Jose Mathew, Sunil Mathew

Department of Mathematics, National Institute of Technology Calicut, Calicut-673601, Kerala, India

Abstract

Mathematically, Mandelbrot defined fractals as sets with non integer Hausdorff dimension which exceeds topological dimension. Later Hutchinson developed the theory of Iterated Function System (IFS) to explain self similarity mathematically. IFS theory and its generalisations were studied intensively from Barnsly onwards. Different forms of self similarities and their topological properties were discussed. They were carried out to higher dimensional spaces and corresponding results were established in the literature.

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