  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 (2017) to alternately obtain duality between star
and plus connected components in the following sense: There is a star connected
cycle of vacant squares attached to and surrounding the finite plus connected
component containing the origin.
