  Inspired by the Weierstrass representation of smooth affine minimal surfaces
with indefinite metric, we propose a constructive process producing a large
class of discrete surfaces that we call discrete affine minimal surfaces. We
show that they are critical points of an affine area functional defined on the
space of quadrangular discrete surfaces. The construction makes use of
asymptotic coordinates and allows defining the discrete analogs of some
differential geometric objects, such as the normal and co normal vector fields,
the cubic form and the compatibility equations.
