  We introduce and analyze some numerical results obtained by the authors
experimentally. These experiments are related to the well known problem about
the distribution of the zeros of Hermite--Pad\'e polynomials for a collection
of three functions $[f_0 \equiv 1,f_1,f_2]$. The numerical results refer to two
cases: a pair of functions $f_1,f_2$ forms an Angelesco system and a pair of
functions $f_1=f,f_2=f^2$ forms a (generalized) Nikishin system. The authors
hope that the obtained numerical results will set up a new conjectures about
the limiting distribution of the zeros of Hermite--Pad\'e polynomials.
