The Peano-Gosper fractal array

This paper investigates the radiation characteristics of a new type of array that is based on the family of space-filling and selfavoiding fractals known as Peano-Gosper curves. The elements of the fractal array are uniformly distributed along a PeanoGosper curve, which leads to a planar array configuration with parallelogram cells that is bounded by a closed Koch curve. These unique properties are exploited in order to develop a design methodology for deterministic arrays that have no grating lobes even when the minimum spacing between elements is increased to at least one wavelength. This leads to a class of arrays that are relatively broad-band when compared to more conventional periodic planar arrays with square or rectangular cells and regular boundary contours. An efficient iterative procedure for calculating the radiation patterns of these PeanoGosper fractal arrays to arbitrary stage of growth P is also introduced in this paper.