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Novel configurations based on Fractal Hilbert curves are proposed for realizing artificial magnetic materials. It is shown that the proposed configuration gives significant rise to miniaturization of artificial unit cells which in turn results in higher homogeneity in the material, and reduction in the profile of the artificial substrate. Analytical formulas are proposed for design and optimization of the presented structures, and are verified through full wave numerical characterization. The electromagnetic properties of the proposed structures are studied in detail and compared to square spiral from the point of view of size reduction, maximum value of the resultant permeability, magnetic loss, and frequency dispersion. To validate the analytical model and the numerical simulation results, an artificial substrate containing second-order Fractal Hilbert curve is fabricated and experimentally characterized using a microstrip-based characterization method.