  We study the distribution of the Frobenius traces on $K3$ surfaces. We
compare experimental data with the predictions made by the Sato--Tate
conjecture, i.e. with the theoretical distributions derived from the theory of
Lie groups assuming equidistribution. Our sample consists of generic $K3$
surfaces, as well as of such having real and complex multiplication. We report
evidence for the Sato--Tate conjecture for the surfaces considered.
