FRACTAL DIMENSIONS OF THE LOGARITHM OF CONTINUOUS FUNCTIONS

Peizhi Liu ()
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Peizhi Liu: School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, P. R. China

FRACTALS (fractals), 2024, vol. 32, issue 01, 1-7

Abstract: This paper investigates the variation of fractal dimensions of continuous functions under operations. It is found that the Box dimension of the logarithm of positive continuous functions remains constant, and any nonzero real power of a positive continuous function can keep fractal dimensions variation closed. The study also discusses the fractal dimension of logarithmic function with bases of fractal functions, and the corresponding fractal dimension is determined by the function with the larger fractal dimension.

Keywords: Fractal Dimension; Continuous Functions; Graph of the Function (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24500038

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