  This paper presents some numerical experiments in relation with the
theoretical study of the ergodic short-term behaviour of discretizations of
expanding maps done in arXiv:2206.07991 [math.DS].
  Our aim is to identify the phenomena driving the evolution of the Cram\'er
distance between the $t$-th iterate of Lebesgue measure by the dynamics $f$ and
the $t$-th iterate of the uniform measure on the grid of order $N$ by the
discretization on this grid. Based on numerical simulations we propose some
conjectures on the effects of numerical truncation from the ergodic viewpoint.
