  The use of statistical methods for the description of complex quantum systems
was primarily motivated by the failure of a line-by-line interpretation of
atomic spectra. Such methods reveal regularities and trends in the
distributions of levels and lines. In the past, much attention was paid to the
distribution of energy levels (Wigner surmise, random-matrix model...).
However, information about the distribution of the lines (energy and strength)
is lacking. Thirty years ago, Learner found empirically an unexpected law: the
logarithm of the number of lines whose intensities lie between 2^kI_0 and
2^{k+1}I_0, I_0 being a reference intensity and k an integer, is a decreasing
linear function of k. In the present work, the fractal nature of such an
intriguing regularity is outlined and a calculation of its fractal dimension is
proposed. Other peculiarities are also presented, such as the fact that the
distribution of line strengths follows Benford's law of anomalous numbers, the
existence of additional selection rules (PH coupling), the symmetry with
respect to a quarter of the subshell in the spin-adapted space (LL coupling)
and the odd-even staggering in the distribution of quantum numbers, pointed out
by Bauche and Coss\'e.
