IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v31y2007i1p179-187.html
   My bibliography  Save this article

Intersection of the Sierpinski carpet with its rational translate

Author

Listed:
  • Dai, Meifeng
  • Tian, Lixin

Abstract

Motivated by Mandelbrot’s idea of referring to lacunarity of Cantor sets in terms of departure from translation invariance, Nekka and Li studied the properties of these translation sets and showed how they can be used for a classification purpose. In this paper, we pursue this study on the Sierpinski carpet with its rational translate. We also get the fractal structure of intersection I(x,y) of the Sierpinski carpet with its translate. We find that the packing measure of these sets forms a discrete spectrum whose non-zero values come only from shifting numbers with a finite triadic expansion. Concretely, when x and y have a finite triadic expansion, a very brief calculation formula of the measure is given.

Suggested Citation

  • Dai, Meifeng & Tian, Lixin, 2007. "Intersection of the Sierpinski carpet with its rational translate," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 179-187.
    • Handle: RePEc:eee:chsofr:v:31:y:2007:i:1:p:179-187
    DOI: 10.1016/j.chaos.2005.09.053
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077905009069
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2005.09.053?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Rani, Mamta & Goel, Saurabh, 2009. "Categorization of new fractal carpets," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 1020-1026.
    2. Dai, Meifeng & Tian, Lixin, 2008. "On the intersection of an m-part uniform Cantor set with its rational translation," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 962-969.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:31:y:2007:i:1:p:179-187. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.