  Here we develop a general statistical procedure for the analysis of finite
two-dimensional (2D) patterns inspired by the analysis of heavy-ion data. The
method is used in the study of publicly available data obtained by the Gaia-ESA
mission. We prove that the procedure can be sensitive to the limits of accuracy
of measurement, and can also clearly identify the real physical effects on the
large background of random distributions. As an example, the method confirms
the presence of binary and ternary star systems in the studied data. At the
same time, the possibility of the statistical detection of the gravitational
microlensing effect is discussed.
