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

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...

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Published inThe European physical journal. B, Condensed matter physics Vol. 97; no. 4; p. 51
Main Authors Husain, Akhlaq, Gumma, Suhas, Sajid, Mohammad, Reddy, Jaideep, Alresheedi, Mohammad T.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2024
Springer
Springer Nature B.V
Subjects
Algorithms
Case studies
Coasts
Complex Systems
Condensed Matter Physics
Dividers
Dynamic programming
Estimation
Flow charts
Fluid- and Aerodynamics
Fractal geometry
Fractals
Geometry
Interpolation
Methods
Multiprocessing
Numerical analysis
Physics
Physics and Astronomy
Python
Recent Advances in Complex Systems
Regular Article - Statistical and Nonlinear Physics
Search algorithms
Simulation
Solid State Physics
Saudi Arabia
Online AccessGet full text
ISSN1434-6028
1434-6036
DOI10.1140/epjb/s10051-024-00696-2

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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 - 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
AbstractList 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 [Formula omitted]program, Python codes, a dynamic programming algorithm, binary search algorithm and the QGIS software.
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 - 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
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 [Formula omitted]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
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-program, Python codes, a dynamic programming algorithm, binary search algorithm and the QGIS software.KSA coastline geometry, methodology and flowchart of the proposed FIF algorithm
ArticleNumber 51
Audience Academic
Author Husain, Akhlaq
Gumma, Suhas
Reddy, Jaideep
Sajid, Mohammad
Alresheedi, Mohammad T.
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Snippet Fractal dimension represents the geometric irregularity of an object with respect to the underlying space and is used for several characterizations. The...
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SubjectTerms Algorithms
Case studies
Coasts
Complex Systems
Condensed Matter Physics
Dividers
Dynamic programming
Estimation
Flow charts
Fluid- and Aerodynamics
Fractal geometry
Fractals
Geometry
Interpolation
Methods
Multiprocessing
Numerical analysis
Physics
Physics and Astronomy
Python
Recent Advances in Complex Systems
Regular Article - Statistical and Nonlinear Physics
Search algorithms
Simulation
Solid State Physics
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Title 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
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