A Mathematical Study on the Application of Box Dimension in Measuring Coastline Length

Coastline evaluation has always been difficult because of the complexity and mathematical functions of shores. Traditional techniques, such as the direct or wall strategy, often ignore coastlines’ nonlinear nature and reject their correct size. This review examines how to identify shores using the Box Dimension from fractal geometry. The box-counting algorithm and higher-resolution world coastline data from the International Self-Steady, Hierarchical, High-Resolution Geography Database (GSHHG) are used to determine the box dimension. The results demonstrate that measuring hard shores, especially in densely populated areas, is more accurate and strongly utilizes the Box Dimension. Also, the assessment examines the computational efficiency of this technique in comparison to regular people. The results suggest that the Box Dimension gives scholars and algebra a more suitable tool for exploring shores, with useful functions in environmental planning and coastal management. These findings provide geographers and mathematicians with more precise tools for analyzing coastline length and complexity.