  We carry out dynamical microwave transport experiments in aperiodic Vogel
spiral arrays of cylinders with high dielectric permittivity. We experimentally
disclose the electromagnetic modal structure of these structures in real space
showing that they simultaneously support long-lived modes with Gaussian,
exponential, and power law spatial decay. This unique modal structure, which
cannot be found in traditional periodic or disordered photonic materials, is
shown to be at the origin of strong localization in Vogel spirals that survives
even in three dimensions. Altogether our results unveil the manifestations of
the rich, unprecedented, spatial structure of electromagnetic modes supported
by aperiodic photonic systems in wave transport and localization.

Disordered Systems and Neural Networks;Optics