Kadyrov Sh.Keulimzhayev A.2025-08-122025-08-122025Kadyrov Sh , Keulimzhayev A / CANTOR SETS AND TOTAL SELF-SIMILARITY / ISCIENCE.IN.UA «Актуальные научные исследования в современном мире» / 20252524-0986https://repository.sdu.edu.kz/handle/123456789/1869We 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 .entotal self-similarityCantor setsfractalsArticle