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 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