  Tile \(\mathbb{R}^2\) into disjoint unit squares \(\{S_k\}_{k \geq 0}\) with
the origin being the centre of \(S_0\) and say that \(S_i\) and \(S_j\) are
star adjacent if they share a corner and plus adjacent if they share an edge.
Every square is either vacant or occupied. In this paper, we use the structure
of the outermost boundaries derived in Ganesan (2015) to alternately obtain
duality between star and plus connected components in the following sense:
There is a plus connected cycle of vacant squares attached to surrounding the
finite star connected component containing the origin. We also obtain the
mutual exclusivity of left right crossings and top down crossings of star and
plus connected components in rectangles.
