Fractal Dimension of Exceptional Sets in Semi-Regular Continued Fractions

Loading...
Thumbnail Image

Date

2025

Journal Title

Journal ISSN

Volume Title

Publisher

faculty of engineering and natural sciences

Abstract

This 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.

Description

Keywords

Regular continued fraction, Lehner expansion, semi-regular continued fraction

Citation

Kadyrov 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 / 2025