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A novel fractal interpolation function algorithm for fractal dimension estimation and coastline geometry reconstruction: a case study of the coastline of Kingdom of Saudi Arabia

Author

Listed:
  • Akhlaq Husain

    (Jamia Millia Islamia)

  • Suhas Gumma

    (BML Munjal University)

  • Mohammad Sajid

    (Qassim University)

  • Jaideep Reddy

    (BML Munjal University)

  • Mohammad T. Alresheedi

    (Qassim University Buraydah)

Abstract

Fractal dimension represents the geometric irregularity of an object with respect to the underlying space and is used for several characterizations. The divider method and the box counting method are two classical methods to compute the fractal dimension of fractals, coastlines, natural objects and other complex systems. In this work, we present a novel, extremely efficient algorithm based on the fractal interpolation function (FIF) method for estimating the fractal dimension of coastlines and for reconstructing the coastline geometry. The algorithm is implemented for the coastline of the Kingdom of Saudi Arabia (KSA) as a case study. For validating the accuracy of the proposed algorithm in estimating the fractal dimension we compare our results with those obtained using the divider and the box-counting method. We also reconstruct the coastline geometry of KSA using our algorithm which generates functions (interpolants) that matches the coastline geometry very accurately. Numerical simulations are obtained using a robust, parallel multi-processing library, an $$R-$$ R - program, Python codes, a dynamic programming algorithm, binary search algorithm and the QGIS software. Graphical abstract KSA coastline geometry, methodology and flowchart of the proposed FIF algorithm

Suggested Citation

  • Akhlaq Husain & Suhas Gumma & Mohammad Sajid & Jaideep Reddy & Mohammad T. Alresheedi, 2024. "A novel fractal interpolation function algorithm for fractal dimension estimation and coastline geometry reconstruction: a case study of the coastline of Kingdom of Saudi Arabia," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(4), pages 1-16, April.
    • Handle: RePEc:spr:eurphb:v:97:y:2024:i:4:d:10.1140_epjb_s10051-024-00696-2
    DOI: 10.1140/epjb/s10051-024-00696-2
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    References listed on IDEAS

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    1. Suleymanov, Arif A. & Abbasov, Askar A. & Ismaylov, Aydin J., 2009. "Fractal analysis of time series in oil and gas production," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2474-2483.
    2. repec:cai:popine:popu_p1998_10n1_0240 is not listed on IDEAS
    3. Chen, Yanguang, 2012. "Fractal dimension evolution and spatial replacement dynamics of urban growth," Chaos, Solitons & Fractals, Elsevier, vol. 45(2), pages 115-124.
    4. Fatemeh Jahanmiri & Dawn Cassandra Parker, 2022. "An Overview of Fractal Geometry Applied to Urban Planning," Land, MDPI, vol. 11(4), pages 1-23, March.
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