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Building structures by low capability robots is a very recent researchdevelopment. A robot (or a mobile agent) is designed as a deterministic finiteautomaton. The objective is to make a structure from a given distribution ofmaterials (\textit{bricks}) in an infinite grid $Z\times Z$. The grid cells maycontain a brick (\textit{full cells}) or it may be empty (\textit{emptycells}). The \textit{field}, a sub-graph induced by the full cells, isinitially connected. At a given point in time, a robot can carry at most onebrick. The robot can move in four directions (north, east, south, and west) andstarts from a \textit{full cell}. The \textit{Manhattan distance} between thefarthest full cells is the \textit{span} of the field.  We consider the construction of a \textit{fort}, a structure with the minimumspan and maximum covered area. On a square grid, a fort is a hollow rectanglewith bricks on the perimeter. We show that the construction of such a fort canbe done in $O(z^2)$ time -- with a matching lower bound $\Omega(z^2)$ -- where$z$ is the number of bricks present in the environment.

Fort Formation by an Automaton