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The Peano-Gosper space-filling curve provides an excellent framework for designing planar antenna array distributions with modular architectures and suppressed sidelobes over a relatively wide bandwidth. The curve consists of a self-avoiding path that intersects a triangular lattice and its construction is based on the iterative application of a generating curve. There exist a number of other recently discovered curves, coined generalized Gosper curves, that possess properties similar to those of the Peano-Gosper curve but are based on larger and more complex generating curves. In this paper these generalized curves will be examined as the framework for antenna array layouts. It will be shown that arrays based on these curves have a number of excellent characteristics while offering modular array configurations and sizes that are not inherent to Peano-Gosper arrays. Moreover, when combined with a simple recursive-perturbation technique, the element distributions of these arrays can be efficiently adjusted to generate designs with bandwidths that far exceed that of standard periodic- and triangular-lattice arrays. The efficacy of this technique will be demonstrated through design examples, including one that has more than a 10:1 bandwidth. Full-wave simulations of a wideband patch array will also be used to investigate the effects of mutual coupling on these array distributions.