  Beacon attraction is a movement system whereby a robot (modeled as a point in
2D) moves in a free space so as to always locally minimize its Euclidean
distance to an activated beacon (which is also a point). This results in the
robot moving directly towards the beacon when it can, and otherwise sliding
along the edge of an obstacle. When a robot can reach the activated beacon by
this method, we say that the beacon attracts the robot. A beacon routing from
$p$ to $q$ is a sequence $b_1, b_2,$ ..., $b_{k}$ of beacons such that
activating the beacons in order will attract a robot from $p$ to $b_1$ to $b_2$
... to $b_{k}$ to $q$, where $q$ is considered to be a beacon. A routing set of
beacons is a set $B$ of beacons such that any two points $p, q$ in the free
space have a beacon routing with the intermediate beacons $b_1, b_2,$ ...,
$b_{k}$ all chosen from $B$. Here we address the question of "how large must
such a $B$ be?" in orthogonal polygons, and show that the answer is "sometimes
as large as $[(n-4)/3]$, but never larger."
