Using the rigorous Green's function spectral method, we systematically investigate the scattering resonances of different types of Vogel spiral arrays of point-like scatterers. By computing the distributions of eigenvalues of the Green's matrix and the corresponding eigenvectors, we obtain important physical information on the spatial nature of the optical modes, their lifetimes and spatial patterns, at small computational cost and for large-scale systems. Finally, we show that this method can be extended to the study of three-dimensional Vogel aperiodic metamaterials and aperiodic photonic structures that may exhibit a richer spectrum of localized resonances of direct relevance to the engineering of novel optical light sources and sensing devices.