  In this paper we study the strengths and limitations of collaborative teams
of simple agents. In particular, we discuss the efficient use of "ant robots"
for covering a connected region on the Z^{2} grid, whose area is unknown in
advance, and which expands at a given rate, where $n$ is the initial size of
the connected region.
  We show that regardless of the algorithm used, and the robots' hardware and
software specifications, the minimal number of robots required in order for
such coverage to be possible is \Omega({\sqrt{n}}).
  In addition, we show that when the region expands at a sufficiently slow
rate, a team of \Theta(\sqrt{n}) robots could cover it in at most O(n^{2} \ln
n) time.
  This completion time can even be achieved by myopic robots, with no ability
to directly communicate with each other, and where each robot is equipped with
a memory of size O(1) bits w.r.t the size of the region (therefore, the robots
cannot maintain maps of the terrain, nor plan complete paths).
  Regarding the coverage of non-expanding regions in the grid, we improve the
current best known result of O(n^{2}) by demonstrating an algorithm that
guarantees such a coverage with completion time of O(\frac{1}{k} n^{1.5} + n)
in the worst case, and faster for shapes of perimeter length which is shorter
than O(n).
