This paper is concerned with a study of the two-dimensional (2-D) time-harmonic scattering by aperiodically-ordered 1-D planar strip arrays based on two-symbol substitutional sequences, under Kirchhoff physical-optics approximation. In this connection, theoretical results from solid-state physics, dwelling on concepts from discrete geometry and number theory, are briefly reviewed and applied to the characterization of the scattering signatures of the above physical configuration. Parametric studies are presented in order to flesh out some of the above concepts and to highlight wave-features which are thought as being representative of a fairly broad class of regular non-periodic scatterers. Potential applications are also envisaged.