We prove that the robber can evade (that is, stay at least unit distance from) at least $\lfloor n/5.889 \rfloor$ cops patroling an $n \times n$ continuous square region, that a robber can always evade a single cop patroling a square with side length $4$ or larger, and that a single cop on patrol can always capture the robber in a square with side length smaller than $2.189\cdots$.