“…Critical modes manifest a power-law localization scaling with highly fragmented multifractal envelopes that were recently employed in multi-mode aperiodic lasing and optical sensing devices [36,[38][39][40][41]. The characteristic features that result from the richer optical phase space spanned by deterministic aperiodic designs found engineering applications to optical sensing, light emission and lasing, photo-detection, optical imaging and nonlinear optical devices [17,24,[42][43][44]. In addition to their importance for key technological applications, the study of deterministic aperiodic nanostructures (DANS) is a highly interdisciplinary and fascinating research field conceptually rooted in several branches of pure and applied mathematics, such as number theory [45,46], symbolic dynamics [47,48], and computational geometry (i.e., tiling and tessellation theory, point patterns and graph theory) [49][50][51][52].…”