https://doi.org/10.1140/epjb/s10051-024-00696-2
Regular Article - Statistical and Nonlinear Physics
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
1
Department of Mathematics, Jamia Millia Islamia, 110025, Delhi, New Delhi, India
2
School of Engineering & Technology, BML Munjal University, 122413, Gurgaon, Haryana, India
3
Department of Mechanical Engineering, College of Engineering, Qassim University, 51452, Buraydah, Al Qassim, Saudi Arabia
4
Department of Civil Engineering, College of Engineering, Qassim University Buraydah, 51452, Buraydah, Al Qassim, Saudi Arabia
Received:
24
January
2024
Accepted:
16
April
2024
Published online:
29
April
2024
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 
program, Python codes, a dynamic programming algorithm, binary search algorithm and the QGIS software.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
