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Fractal two-dimensional electromagnetic bandgap (EBG) materials are proposed and studied by means of a full-wave method developed for diffraction gratings. Such technique allows us to characterize, In an accurate and rapidly convergent way, the transmission and reflection properties of periodic fractal structures with an arbitrary geometry in the unit cell. Both polarization cases can be treated. A validation of the employed method is performed through a comparison with theoretical results and experimental data taken from the literature; the convergence properties of our method when applied to fractal EBG materials are checked. In particular, three different fractal EBGs are considered here. Numerical results are reported for the transmission efficiency as a function of the frequency and the incidence angle. Typical effects due to the fractal geometry are observed, like multiband behavior and enlargement of stopbands.