Kadyrov Sh.Kazin A.Duisen S.2025-08-112025-08-112025Kadyrov Sh , Kazin A , Duisen S / Fractal Dimension of Exceptional Sets in Semi-Regular Continued Fractions / Journal of Emerging Technologies and Computing (JETC), Vol. 1 No. 1 / 2025https://repository.sdu.edu.kz/handle/123456789/1856This paper examines how the average value of the sequence bn in the Lehner expansion of a real number x influences its box dimension. Our primary objective is to analyze how variations in the average of bn impact the box dimension, which serves as a measure of the complexity of the sequence. Using the box-counting method, we numerically estimate the box dimension and explore its relationship with the fractal nature of Lehner expansions.enRegular continued fractionLehner expansionsemi-regular continued fractionArticle