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Fractal Dimensions Of Sets Defined By Digit Restrictions In „ 2

Author

Listed:
  • LIPENG WANG

    (School of Mathematical Sciences, East China Normal University, 500 Dongchuan Rd., Shanghai 200241 P. R. China)

  • WENXIA LI

    (School of Mathematical Sciences, East China Normal University, 500 Dongchuan Rd., Shanghai 200241 P. R. China)

Abstract

We introduce a class of sets defined by digit restrictions in â„ 2 and study its fractal dimensions. Let ES,D be a set defined by digit restrictions in â„ 2. We obtain the Hausdorff and lower box dimensions of ES,D. Under some condition, we gain the packing and upper box dimensions of ES,D. We get the Assouad dimension of ES,D and show that it is 2 if and only if ES,D contains arbitrarily large arithmetic patches. Under some conditions, we study the upper spectrum, quasi-Assouad dimension and Assouad spectrum of ES,D. Finally, we give an intermediate value property of fractal dimensions of the class of sets.

Suggested Citation

  • Lipeng Wang & Wenxia Li, 2023. "Fractal Dimensions Of Sets Defined By Digit Restrictions In „ 2," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(07), pages 1-24.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:07:n:s0218348x23500743
    DOI: 10.1142/S0218348X23500743
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