Cantor diffractals and lacunarity

We examine diffraction by Cantor apertures (Cantor diffractals) including a new class of Cantor targets based on a polyadic Cantor set described by several fractal descriptors. We find scaling properties characteristic of these apertures and examine their radiation patterns through the introduction of twist plots which allows one to find windows of lacunarity and fractal dimension for which these apertures exhibit desired behavior such as low sidelobes. We find these diffractals have distinctive subfractal, fractal and superfractal radiation regimes with boundaries that are predicted from the diffractal geometry.