  We show that when the standard techniques for calculating fractal dimensions
in empirical data (such as the box counting) are applied on uniformly random
structures, apparent fractal behavior is observed in a range between physically
relevant cutoffs. This range, spanning between one and two decades for
densities of 0.1 and lower, is in good agreement with the typical range
observed in experiments. The dimensions are not universal and depend on
density. Our observations are applicable to spatial, temporal and spectral
random structures, all with non-zero measure. Fat fractal analysis does not
seem to add information over routine fractal analysis procedures. Most
significantly, we find that this apparent fractal behavior is robust even to
the presence of moderate correlations. We thus propose that apparent fractal
behavior observed experimentally over a limited range in some systems, may
often have its origin in underlying randomness.
