  Any constructive continuous function must have a gradually varied
approximation in compact space. However, the refinement of domain for
$\sigma-$-net might be very small. Keeping the original discretization (square
or triangulation), can we get some interesting properties related to gradual
variation? In this note, we try to prove that many harmonic functions are
gradually varied or near gradually varied; this means that the value of the
center point differs from that of its neighbor at most by 2. It is obvious that
most of the gradually varied functions are not harmonic.This note discusses
some of the basic harmonic functions in relation to gradually varied functions.
