IDEAS home Printed from https://ideas.repec.org/a/wsi/fracta/v32y2024i05ns0218348x24500968.html
   My bibliography  Save this article

On Self-Similarity Of Quadrangle

Author

Listed:
  • JIAJUN XU

    (School of Mathematics and Statistics, Ningbo University, Ningbo, P. R. China)

  • JINGHUA XI

    (Department of Mathematics, Southern University of Science and Technology, Shenzhen, P. R. China)

  • KAN JIANG

    (School of Mathematics and Statistics, Ningbo University, Ningbo, P. R. China)

Abstract

Wen [Some problems in fractal geometry, in Report in Chinese Conference on Fractal Geometry and Dynamical Systems, 2023] posed the following questions: when a quadrangle is a self-similar set with the open set condition (OSC). It is well known that any convex quadrangle is a self-similar set. For the concave quadrangles, this case is more complicated. Loosely speaking, some concave polygons may be not self-similar. In this paper, we prove two results. First, we give a necessary and sufficient condition such that a concave quadrangle is a self-similar set. Moreover, we also give a necessary condition for a concave quadrangle to be a self-similar set with the OSC. For the convex quadrangle, we investigate the trapezoid. We show under some condition that the trapezoid is a self-similar set with the OSC. In particular, for any trapezoid, if the ratio of the lengths of two bases is rational, then the trapezoid is a self-similar set with the OSC.

Suggested Citation

  • Jiajun Xu & Jinghua Xi & Kan Jiang, 2024. "On Self-Similarity Of Quadrangle," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(05), pages 1-7.
    • Handle: RePEc:wsi:fracta:v:32:y:2024:i:05:n:s0218348x24500968
    DOI: 10.1142/S0218348X24500968
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0218348X24500968
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0218348X24500968?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.

    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:wsi:fracta:v:32:y:2024:i:05:n:s0218348x24500968. 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: Tai Tone Lim (email available below). General contact details of provider: https://www.worldscientific.com/worldscinet/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.