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The Peano-Gosper space-filling curve provides an excellent framework for designing broadband planar antenna arrays with highly modular architectures. Uniformly distributing elements along the curve leads to an element distribution with a triangular lattice that has an irregular fractal boundary contour. This boundary contour allows for a modular subarray configuration and better sidelobe suppression than conventional triangular lattice arrays with a regular boundary contour. While they have a greater bandwidth than square-lattice distributions, arrays based on a triangular lattice still possess a rather limited bandwidth for beam steering applications due to the formation of grating lobes. In this communication it will be shown that the beam steering capabilities of the Peano-Gosper array can be enhanced by introducing perturbations into the basic recursive array generation scheme. With the proper implementation, the perturbed arrays retain the attractive features of modularity and recursive beamforming that are associated with the standard Peano-Gosper array. Examples will be presented for several stages of Peano-Gosper arrays that were designed for 2:1 broadband performance while scanning within a 30?? conical volume. Full-wave simulations will be used to examine the effects of mutual coupling on these aperiodic array layouts.