Fractal dimension of 1/(f to the alpha power) noises

An extended reticular cell counting method is proposed in order to increase the accuracy in the determination of the fractal dimension of a signal. The method can be used to determine the fractal dimension of a surface, and will allow the use of the fractal dimension to characterize random signals and random surfaces. As an example, the fractal number D is studied for noises with a spectral density of the shape 1/(f to the alpha power). It is shown that the fractal dimension decreases linearly for low values of the spectrum parameter (alpha less than 1.5) and tends to unity for high values (alpha higher than 2.5).