A simple method to estimate fractal dimension of mountain surfaces

TL;DR

This paper introduces a straightforward method to estimate the fractal dimension of mountain surfaces using satellite images of lakes, providing a practical way to quantify topographical irregularity.

Contribution

The paper presents a novel, simple approach to determine mountain surface fractal dimensions through satellite image analysis of lake boundaries.

Findings

Fractal dimension of mountain surfaces can be estimated from lake boundary images.

The method is easy to implement with available satellite imagery and image analysis software.

This approach aids in validating models of mountain formation.

Abstract

Fractal surfaces are ubiquitous in nature as well as in the sciences. The examples range from the cloud boundaries to the corroded surfaces. Fractal dimension gives a measure of the irregularity in the object under study. We present a simple method to estimate the fractal dimension of mountain surface. We propose to use easily available satellite images of lakes for this purpose. The fractal dimension of the boundary of a lake, which can be extracted using image analysis softwares, can be determined easily which gives the estimate of the fractal dimension of the mountain surface and hence a quantitative characterization of the irregularity of the topography of the mountain surface. This value will be useful in validating models of mountain formation