The discovery of “quasi-crystals,” whose X-ray diffraction patterns reveal certain unusual features which do not conform with spatial periodicity, has motivated studies of the wave-dynamical implications of “aperiodic order.” This paper discusses various aperiodic configurations generated by Rudin-Shapiro (RS) sequences. These RS sequences constitute ones of the simplest conceivable examples of deterministic aperiodic geometries featuring random-like (dis)order. The scattering properties of aperiodically-ordered thinned 2-D patch arrays based on RS sequences are analyzed by using physical optics approximation. Compared to a periodic case, RS-based antenna array is found to have a substantial reduction in the magnitude of the backscattering component of the scattered signal with half of the elements and the same magnitude of specular reflection. This property is verified by illustrative numerical parametric studies.