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A note on fractal dimensions of graphs of certain continuous functions

Author

Listed:
  • Liu, Peizhi
  • Yu, Binyan
  • Liang, Yongshun

Abstract

This article investigates fractal dimensions variation of fractal functions under certain operations, which corroborates the conjecture raised in our previous work Yu and Liang (2024) [1]. It has been shown that when polynomial operations are applied to the independent variable of a function, the fractal dimension of the function’s graph remains unchanged. This finding holds significance for the construction of fractal functions.

Suggested Citation

  • Liu, Peizhi & Yu, Binyan & Liang, Yongshun, 2024. "A note on fractal dimensions of graphs of certain continuous functions," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:chsofr:v:188:y:2024:i:c:s0960077924009652
    DOI: 10.1016/j.chaos.2024.115413
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    References listed on IDEAS

    as
    1. Verma, Manuj & Priyadarshi, Amit, 2023. "Graphs of continuous functions and fractal dimensions," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    2. Peizhi Liu & Yumeng Du & Yongshun Liang, 2023. "Fractal Dimension Of Product Of Continuous Functions With Box Dimension," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(03), pages 1-8.
    3. 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.
    4. Binyan Yu & Yongshun Liang, 2024. "Research On Fractal Dimensions And The Hã–Lder Continuity Of Fractal Functions Under Operations," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(03), pages 1-28.
    5. Binyan Yu & Yongshun Liang, 2023. "Fractal Dimension Variation Of Continuous Functions Under Certain Operations," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(05), pages 1-16.
    Full references (including those not matched with items on IDEAS)

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