In this paper,
Miller's correlation based model of orientation selectivity
is studied, in particular, a development of
an oriented receptive field is considered and analyzed mathematically.

Our computer simulations show that
(1) the final shape of a receptive field most likely appears
just after the first update of synaptic weights, and
(2) synaptic weights are updated monotonously
preserving the shape of a receptive field
that is already determined
at the first step.
We try to explain these two properties
and give some mathematical justifications by considering
a simplified model.

As a result, we show that
(1) if a learning efficacy is small enough,
synaptic weights almost always grow monotonously, and
(2) if the width of an arbor and the range of a correlation is similar,
then the increment at the first step
forms three separated subregions of {\small\it ON} and {\small\it OFF}.
Moreover,
we also show that if the range of a correlation
is much smaller than the width of an arbor,
then the incremental forms several small clusters of
{\small\it ON} and {\small\it OFF}.