Generalization To More Than One Dimension
The spectrum of pink noise is 1/f only for one-dimensional signals. For two-dimensional signals, e.g., images, the spectrum is reciprocal to f2. In general, in an n-dimensional system, the spectrum is reciprocal to fn. For higher-dimensional signals it is still true (by definition) that each octave carries an equal amount of noise power. The frequency spectrum of two-dimensional signals, for instance, is also two-dimensional, and the area covered by succeeding octaves is four times as large.
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