Fractal characteristics of geomorphological heterogeneity in Xisha Islands waters under Multiple Linear Regression

Wang Xu-Li

doi:10.15446/esrj.v25n1.94076

Abstract

Based on the obvious anisotropy of Xisha Islands waters topography, the uneven fractal characteristics of Xisha Islands waters topography are studied by using multivariate linear expression. Using multiple linear regression analysis method to extract the projection of heterogeneous characteristic factors, the geometric heterogeneous characteristics of Xisha Islands waters are obtained. The fractal feature of landform is studied based on projection coverage method, and the non-isotropic body irregularity in Xisha Islands waters is measured. Experimental results show that this method can effectively analyze the non-uniform fractal characteristics of the Xisha Islands waters. The fractal dimension of different types of landforms in Xisha Islands in the corresponding region is high mountain area > medium and low mountain area > basin area, which reflects the difference of surface roughness or complexity of different types of landforms. The calculated fractal dimension is helpful to reveal the heterogeneity of general geomorphological features in different development stages.

Highlights

For human beings, the most common phenomena in nature, such as the varied landforms and the turbulence in the river, are unpredictable and lack rules
In the Shidao water area of the Xisha Islands, the fractal dimension values of different types of landforms in the corresponding interval are as follows: water area in high mountain area > water area in middle and low mountain area > water area in basin area, which reflects the difference of surface roughness or complexity of different types of landforms
Fractal theory is applied to landforms

Summary

Introduction

The most common phenomena in nature, such as the varied landforms and the turbulence in the river, are unpredictable and lack rules. With the creation of Newton’s classical mechanics, Einstein’s theory of relativity, and the development of quantum mechanics, human beings have made brilliant achievements in Natural Science (Liu & Jiang, 2020; ArangurenRiano et al, 2018). Triangles, rectangles, squares, circles and so on, as practical techniques or tools of mathematics, are gradually created in the development of human social practice, and form arithmetic, algebra, geometry, trigonometry and calculus. Geometry is the first subject to rise from empirical knowledge to theoretical knowledge, and its typical representative is Euclid’s “geometric original” (Padisak et al, 2016). It is the first work in the history of mathematics to systematically discuss geometry by using axioms and methods. For quite a long time, geometry, as the science of describing the form of things, has been regarded as the only real mathematics and the model of scientific rigor (Gu et al, 2018; Hu et al, 2018; Kong et al, 2018; Zhang, 2020)

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