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The extremely remarkable properties of angle independence exhibited by an innovative SAR product, the fractal dimension map estimated from a single SAR image, are discussed. The theoretical analysis is supported by a noticeable data set of actual SAR images acquired, with look angles varying from 20° to 45°, in the stripmap operational mode by the COSMO-SkyMed constellation. The behavior of the fractal dimension maps at different look angles is discussed for both natural and urban scenarios and emphasis is also posed on areas within the same image that, according to the scene macroscopic topography, are characterized by different incidence angles. The whole analysis is aimed at highlighting, on the one hand, the specific independencies of natural surface fractal dimension maps from the look angle and from the local incidence angle, which can be very useful in information extraction and SAR post-processing techniques and, on the other hand, the different fractal dimension maps behavior whereas urban areas are analyzed.