Box dimension of the border of Kingdom of Saudi Arabia

Mohammad Sajid; Akhlaq Husain; Jaideep Reddy; Mohammad T Alresheedi; Sulaiman A Al Yahya; Ahmed Al-Rajy

doi:10.1016/j.heliyon.2023.e14846

Box dimension of the border of Kingdom of Saudi Arabia

Heliyon. 2023 Mar 23;9(4):e14846. doi: 10.1016/j.heliyon.2023.e14846. eCollection 2023 Apr.

Authors

Mohammad Sajid¹, Akhlaq Husain², Jaideep Reddy³, Mohammad T Alresheedi⁴, Sulaiman A Al Yahya¹, Ahmed Al-Rajy⁴

Affiliations

¹ Department of Mechanical Engineering, College of Engineering, Qassim University, Buraydah, 51452, Saudi Arabia.
² Department of Applied Sciences, BML Munjal University, Gurgaon, 122413, Haryana, India.
³ School of Engineering & Technology, BML Munjal University, Gurgaon, 122413, Haryana, India.
⁴ Department of Civil Engineering, College of Engineering, Qassim University, Buraydah, 51452, Saudi Arabia.

Abstract

Fractal dimension unlike topological dimension is (usually) a non-integer number which measures complexity, roughness, or irregularity of an object with respect to the space in which the set lies. It is used to characterize highly irregular objects in nature containing statistical self-similarity such as mountains, snowflakes, clouds, coastlines, borders etc. In this article, box dimension (a version of fractal dimension) of the border of Kingdom of Saudi Arabia (KSA) is computed using a multicore parallel processing algorithm based on the classical box-counting method. A power law relation is obtained from numerical simulations which relates the length of the border with the scale size and provides a very close estimate of the actual length of the KSA border within the scaling regions and scaling effects on the length of KSA border are considered. The algorithm presented in the article is shown to be highly scalable and efficient and the speedup of the algorithm is computed using Amdahl's and Gustafson's laws. For simulations, a high performance parallel computer is employed using Python codes and QGIS software.

Keywords: Border; Box dimension; Box-counting method; Fractal dimension; Multicore processing.