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A remarkable fact for the box dimensions of fractal interpolation curves of R3

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  • Ri, SongIl

Abstract

In this paper, we give the fractal interpolation curves generated on the Koch curve by Hölder continuous functions and function vertical scaling factors, and at the same time, we present the estimation method of box dimensions of curves of R3 through the estimation of lower and upper box dimensions of obtained curves, where a remarkable fact is that the box dimensions are dependent not only on function vertical scaling factors but also on Hölder exponent of harmonic functions on the Koch curve.

Suggested Citation

  • Ri, SongIl, 2021. "A remarkable fact for the box dimensions of fractal interpolation curves of R3," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    • Handle: RePEc:eee:chsofr:v:151:y:2021:i:c:s0960077921005592
    DOI: 10.1016/j.chaos.2021.111205
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    References listed on IDEAS

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    1. Amo, Enrique de & Díaz Carrillo, Manuel & Fernández Sánchez, Juan, 2013. "PCF self-similar sets and fractal interpolation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 92(C), pages 28-39.
    2. Ri, SongIl, 2020. "Fractal functions on the Sierpinski Gasket," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    3. Yun, CholHui & Ri, MiGyong, 2020. "Box-counting dimension and analytic properties of hidden variable fractal interpolation functions with function contractivity factors," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    4. Yun, Chol-hui & O, Hyong-chol & Choi, Hui-chol, 2014. "Construction of fractal surfaces by recurrent fractal interpolation curves," Chaos, Solitons & Fractals, Elsevier, vol. 66(C), pages 136-143.
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