A GIS-Based Spatial Null Model Framework for Evaluating Logarithmic Spiral Patterns in Point Sets

Abstract

This study develops and applies a GIS-based spatial null model framework to evaluate whether observed point sets exhibit constrained logarithmic spiral patterns beyond what would be expected under spatial randomness and alternative structured configurations. We integrate exhaustive enumeration, Monte Carlo randomization, and constraint-preserving null ensembles within a GIS environment that explicitly limits geometric degrees of freedom to test multiple candidate geometric hypotheses. Spatial datasets of summit coordinates were prepared and analyzed as standardized GIS point layers to demonstrate practical implementation. Null models preserve varying degrees of spatial constraints to reflect alternative generative processes. The framework quantifies departures from each null distribution using robust pattern statistics, emphasizing reproducibility and transferability across spatial datasets. Results highlight the approach’s capacity to distinguish between random, constraint-driven, and highly structured spiral configurations in point patterns. This methodology operationalizes falsification-based spatial hypothesis testing in GIS research and offers a generalizable toolset for pattern analysis in geographic information systems.