IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i2p384-d1032287.html
   My bibliography  Save this article

Estimation of Citarum Watershed Boundary’s Length Based on Fractal’s Power Law by the Modified Box-Counting Dimension Algorithm

Author

Listed:
  • Michael Lim

    (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Jawa Barat, Indonesia)

  • Alit Kartiwa

    (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Jawa Barat, Indonesia)

  • Herlina Napitupulu

    (Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Sumedang 45363, Jawa Barat, Indonesia)

Abstract

This research aimed to estimate the length of the Citarum watershed boundary because the data are still unknown. We used the concept of fractal’s power law and its relation to the length of an object, which is still not described in other research. The method that we used in this research is the Box-Counting dimension. The data were obtained from the geographic information system. We found an equation that described the relationship between the length and fractal dimension of an object by substituting equations. Following that, we modified the algorithm of Box-Counting dimension by consideration of requiring a high-resolution image, using the Canny edge detection so that the edges look sharper and the dimension values are more accurate. A Box-Counting program was created with Python based on the modified algorithm and used to execute the Citarum watershed boundary’s image. The values of ε and N were used to calculate the fractal dimension and the length for each scale by using the value of C = 1 , assuming the ε as the ratio between the length of box and the length of plane. Finally, we found that the dimension of Citarum watershed boundary is approximately 1.1109 and its length is 770.49 km.

Suggested Citation

  • Michael Lim & Alit Kartiwa & Herlina Napitupulu, 2023. "Estimation of Citarum Watershed Boundary’s Length Based on Fractal’s Power Law by the Modified Box-Counting Dimension Algorithm," Mathematics, MDPI, vol. 11(2), pages 1-12, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:384-:d:1032287
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/2/384/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/2/384/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Alison K. Cheeseman & Edward R. Vrscay, 2022. "Estimating the Fractal Dimensions of Vascular Networks and Other Branching Structures: Some Words of Caution," Mathematics, MDPI, vol. 10(5), pages 1-21, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Francisco Martinez & Hermann Manriquez & Alberto Ojeda & Gabriel Olea, 2022. "Organization Patterns of Complex River Networks in Chile: A Fractal Morphology," Mathematics, MDPI, vol. 10(11), pages 1-23, May.
    2. Francisco Martínez & Bastian Sepúlveda & Hermann Manríquez, 2023. "Fractal Organization of Chilean Cities: Observations from a Developing Country," Land, MDPI, vol. 12(2), pages 1-21, January.

    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:gam:jmathe:v:11:y:2023:i:2:p:384-:d:1032287. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.