IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v113y2018icp16-24.html
   My bibliography  Save this article

Unreliable determination of fractal characteristics using the capacity dimension and a new method for computing the information dimension

Author

Listed:
  • Liu, Jingshou
  • Ding, Wenlong
  • Dai, Junsheng
  • Zhao, Gang
  • Sun, Yaxiong
  • Yang, Haimeng

Abstract

Fractal theory has been widely applied in a variety of disciplines to understand the theory behind chaotic phenomena based on internal self-similarity. In this study, three ideal geological models are used to analyze the unreliability of the capacity dimension in the fractal calculation of geological bodies with different scales. Additionally, by varying the side length r of the statistical units, the geological meanings of the fractal dimension D and the correlation coefficient R2 are discussed. The points of information (POIs) are densely filled by binarizing the geological bodies to black/white. Based on the optimized r of a geological body, an algorithm is derived that divides the grids of the statistical units to determine the probability of the POIs falling into different grids. The information dimension (DI) and R2 of a geological body are obtained by fitting the variable data. An example calculation of the information dimension field in the Jinhu sag is presented to demonstrate the methodology and to test its reliability. The results show that determining the appropriate side length of the statistical unit is key to evaluating the fractal calculation. Compared to the capacity dimension, DI is more reliable in the fractal calculation of multi-scale geological bodies; DI is thereby the preferred fractal dimension to use in the analyses of these types of geological bodies.

Suggested Citation

  • Liu, Jingshou & Ding, Wenlong & Dai, Junsheng & Zhao, Gang & Sun, Yaxiong & Yang, Haimeng, 2018. "Unreliable determination of fractal characteristics using the capacity dimension and a new method for computing the information dimension," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 16-24.
    • Handle: RePEc:eee:chsofr:v:113:y:2018:i:c:p:16-24
    DOI: 10.1016/j.chaos.2018.05.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077918302534
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2018.05.008?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.

    References listed on IDEAS

    as
    1. Chamorro-Posada, Pedro, 2016. "A simple method for estimating the fractal dimension from digital images: The compression dimension," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 562-572.
    2. Ian Enting, 2008. "G. Cello and B. D. Malamud (eds): Review of: Fractal Analysis for Natural Hazards (Geological Society, Special Publication 261)," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 45(1), pages 137-138, April.
    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. Arce, Walker & Pierce, James & Velcsov, Mihaela Teodora, 2021. "A single-scale fractal feature for classification of color images: A virus case study," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    2. Zuo, Xue & Tang, Xiang & Zhou, Yuankai, 2020. "Influence of sampling length on estimated fractal dimension of surface profile," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).

    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:113:y:2018:i:c:p:16-24. 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: 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.