  It is known that minimal surfaces in Euclidean space can be represented in
terms of holomorphic functions. For example, we have the well-known Weierstrass
representation, where part of the holomorphic data is chosen to be the
stereographic projection of the normal of the corresponding surface, and also
the Bj\"orling representation, where it is prescribed a curve on the surface
and the unit normal on this curve. In this work, we are interested in the
holomorphic representation of minimal surfaces in simply isotropic space, a
three-dimensional space equipped with a rank 2 metric of index zero. Since the
isotropic metric is degenerate, a surface normal cannot be unequivocally
defined based on metric properties only, which leads to distinct definitions of
an isotropic normal. As a consequence, this may also lead to distinct forms of
a Weierstrass and of a Bj\"orling representation. Here, we show how to
represent simply isotropic minimal surfaces in accordance with the choice of an
isotropic surface normal.
