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Several novel antenna structures based on a combination of regular and fractal shaped elements are presented. It has been shown with case studies that the performance of the antennas can be optimized by judicious choice of fractal geometries. Though the fractal elements have a high degree of regularity, introduction of certain irregularities in the structures can result in improved performance of the antennas. Both directly coupled and parasitically coupled fractal elements have been used to construct these novel antenna structures.