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There has been considerable interest in the radiation characteristics of self-scalable and self-similar planar arrays. For instance, array configurations based on Sierpinski carpets have been considered. The properties of self-scalable concentric circular Weierstrass arrays and self-similar concentric circular Cantor arrays have also been investigated. We present an alternative design methodology for the mathematical construction of self-scalable and self-similar planar arrays. The technique is very general and consequently provides much more flexibility in the design of fractal and related arrays when compared to other approaches previously considered in the literature. This is primarily due to the fact that the generator in this case is based on a concentric circular ring array.