Fractal Geometry in Geomorphology: Quantifying Coastline Complexity and Erosion Patterns
Authors
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Nick Edwards
Oceanic Study Center
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Helen Howard
Pinnacle College
https://orcid.org/0009-0000-0000-0000
Abstract
Mandelbrot's observation that coastlines are not smooth but possess self-similar, fractal properties revolutionized geomorphology. This study moves beyond simple fractal dimension (D) calculations to develop a multi-scalar framework for quantifying coastline complexity and its relationship to erosion and deposition patterns. Using high-resolution satellite imagery (LiDAR and multispectral data), we apply wavelet-based fractal analysis to measure how the fractal dimension changes across different spatial scales. This multi-scalar signature allows us to differentiate between coastlines dominated by various geomorphic processes (e.g., tectonic uplift, deltaic progradation, tidal erosion). We establish a robust mathematical correlation between a declining fractal dimension and increased coastal vulnerability to sea-level rise. This 'Math Earth' approach provides a novel, quantitative tool for coastal zone management, enabling the identification of erosion hotspots and the optimization of coastal defense strategies by treating the coastline as the complex dynamical system it is.
Copyright (c) 2026 Nick Edwards, Helen Howard (Author)
This work is licensed under a Creative Commons Attribution 4.0 International License.