Fractal Dimension of Exceptional Sets in Semi-Regular Continued Fractions
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Date
2025
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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.
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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