Measuring the geometry of natural landscapes is often straightforward, yet highly irregular terrains challenge traditional approaches to quantification. These irregularities are frequently fractal in nature, exhibiting self-similar patterns that complicate conventional measurement techniques. This study investigates the fractal dimension of Arctic terrain as a metric for describing surface roughness and detecting environmental change. Using the box-counting method applied to Digital Elevation Models (DEMs) sourced from ArcticDEM satellite data (2008–2025), we analyze select Greenland regions to assess how fractal geometry can enhance terrain monitoring. By constraining data to July samples within a 10 km radius, we reduced confounding factors such as seasonal variation. Python-based algorithms generate two-dimensional slope estimates and three-dimensional visualizations, enabling fractal dimension estimation across varying box sizes. Preliminary results confirm that smaller box sizes yield more reliable representations of terrain complexity, though challenges arise from incomplete box coverage. This approach demonstrates potential for identifying subtle terrain shifts linked to climate change, such as glacial retreat and erosion, that may be missed by conventional metrics. Beyond the Arctic, the methodology offers broader applicability for analyzing diverse landscapes affected by environmental pressures. Ultimately, fractal dimension analysis provides a bridge between mathematics and climate science, offering a sensitive, scalable tool for detecting and quantifying terrain change in an era of accelerating global transformation.