The Earth's topography generally obeys fractal statistics: after either one- or two-dimensional Fourier transforms the amplitudes have a power law dependence on wave number. The slope gives the fractal dimension, and the unit wave number amplitude is a measure of the roughness. In this study, digitized topography for the state of Arizona (7 points/km) has been used to obtain maps of fractal dimension and roughness amplitude. The roughness amplitude correlates well with variations in relief and is a promising parameter for the quantitative classification of geomorphology. Significant variations in fractal dimension are also found. For Arizona the mean fractal dimension for two-dimensional Fourier spectral analyses is D=2.09; for one-dimensional Fourier spectral analyses the mean fractal dimension is D=1.52, close to the Brown noise value D=1.5. Synthetic two-dimensional images have also been generated for a range of D values. For D=2.1, the synthetic image has a mean one-dimensional spectral fractal dimension D=1.56, consistent with our results for Arizona. These results are also consistent with those of previous authors and show that it is not appropriate to subtract one from the two-dimensional fractal dimension of topography in order to obtain the one-dimensional fractal dimension. ¿ American Geophysical Union 1989