CANTOR SETS AND TOTAL SELF-SIMILARITY

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Date

2025

Journal Title

Journal ISSN

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ISCIENCE.IN.UA «Актуальные научные исследования в современном мире»

Abstract

We study overlapping Cantor sets with parameter and classify the situations when these fractal sets are totally self-similar. More precisely, we consider iterated function system consisting of three functions , and and the fractal set it generates in the real line. We define what totally self-similar means and show for that the fractal set is totally self-similar if and only if it is in the form for some positive integer . We mainly rely on the recent work of Dajani, Kong, and Yao where they consider the analogous problem for .

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Keywords

total self-similarity, Cantor sets, fractals

Citation

Kadyrov Sh , Keulimzhayev A / CANTOR SETS AND TOTAL SELF-SIMILARITY / ISCIENCE.IN.UA «Актуальные научные исследования в современном мире» / 2025