A Complex Polynomial Exponential Model for Mountain Ridge Line Geometry

This paper presents a novel analytical formulation of mountain ridge line geometry using an exponential function of a complex-valued polynomial. The proposed model expresses the ridge height as: where the real components ak determine the general profile and the imaginary components bk introduce asymmetry, curvature, and local fluctuations. This approach enables a unified description of ridge structures with both symmetric and non-symmetric features. The model is particularly well-suited for interpreting natural forms such as crater rims, volcanic domes, and tectonic fold ridges. The exponential formulation allows modeling of steep elevation changes or wave-like growth patterns resulting from geological or impact-related processes. This work bridges mathematical compactness with geophysical relevance, offering a new tool for theoretical and applied geomorphology.