The development of exotic new materials, such as metamaterials, has created strong interest within the electromagnetics (EM) community for possible new phenomenologies and device applications, with particular attention to periodicity-induced phenomena, such as photonic bandgaps. Within this context, motivated by the fairly recent discovery in X-ray crystallography of “quasi-crystals”, whose diffraction patterns display unusual characteristics that are associated with “aperiodic order”, we have undertaken a systematic study of how these exotic effects manifest themselves in the radiation properties of aperiodically configured antenna arrays. The background for these studies, with promising example configurations, has been reported in a previous publication [V. Pierro et al., IEEE Trans. Antennas Propag., vol. 53, pp. 635-644, Feb. 2005]. In this paper, we pay attention to various configurations generated by Rudin-Shapiro (RS) sequences, which constitute one of the simplest conceivable examples of deterministic aperiodic geometries featuring random-like (dis)order. After presentation and review of relevant background material, the radiation properties of one-dimensional RS-based antenna arrays are analyzed, followed by illustrative numerical parametric studies to validate the theoretical models. Design parameters and potential practical applications are also given attention.