Spatial and Spectral Analysis of Metallic Mean Vogel Arrays: High-Resolution 2D FFT Empirical Observations

This report documents the geometric and spectral properties of Vogel arrays generated via the sequence of metallic means. By mapping the physical coordinates and applying a high-resolution Two-Dimensional Fast Fourier Transform (2D FFT), the spatial momentum distribution of these deterministic aperiodic structures is evaluated. The empirical measurements quantitatively present the intensity of the k=0 momentum core and the topology of the surrounding frequency-depleted regions (bandgaps) under both ideal and structurally deficient conditions.