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Fractal Dimensions Of The Logarithm Of Continuous Functions

Author

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  • PEIZHI LIU

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

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.

Suggested Citation

  • Peizhi Liu, 2024. "Fractal Dimensions Of The Logarithm Of Continuous Functions," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(01), pages 1-7.
    • Handle: RePEc:wsi:fracta:v:32:y:2024:i:01:n:s0218348x24500038
    DOI: 10.1142/S0218348X24500038
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