Spatial and spectral descriptions of stationary Gaussian fractals

Abstract
A general treatment of stationary Gaussian fractals is presented. Relations are established between the fractal properties of an n-dimensional random field and the form of its correlation function and power spectrum. These relations are used to show that the second-order parameter H commonly used to describe fractal texture is insufficient to characterize all fractal aspects of the field. A larger set of measures -- based on the power spectrum -- is shown to provide a more complete description of fractal texture.
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