Numerical Fractal Analysis of Exceptional Sets in the Lehner Expansion: Article

Symbat Duisen; Aiken Kazin; Shirali  Kadyrov

doi:10.47344/q46xe557

Article

Numerical Fractal Analysis of Exceptional Sets in the Lehner Expansion

Authors

Symbat Duisen SDU University Author https://orcid.org/0009-0009-7514-0503
Aiken Kazin Author https://orcid.org/0000-0002-9658-9723
Shirali Kadyrov Author https://orcid.org/0000-0002-8352-2597

DOI:

https://doi.org/10.47344/q46xe557

Keywords:

Regular continued fraction, Lehner expansion, semi-regular continued fraction,fractal dimension, box dimension.

Abstract

This paper examines how the average value of the sequence b_n 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.

Additional Files

Published

2025-06-30

Issue

Vol. 1 No. 1 (2025): Journal of Emerging Technologies and Computing (JETC)

Section

Mathematics with applied aspects

How to Cite

Duisen, S., Kazin, A., & Kadyrov, S. (2025). Numerical Fractal Analysis of Exceptional Sets in the Lehner Expansion: Article. Journal of Emerging Technologies and Computing, 1(1). https://doi.org/10.47344/q46xe557

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