Minimum-move maps

Label every square with the fewest moves a piece needs to reach it from a fixed start. This distance map is a graph idea: squares are vertices, legal moves are edges, and the label is the shortest-path distance. Build it in waves: the start is $0$, every square one move away is $1$, every new square reachable from those is $2$, and so on.

For a rook the map is simple, since any square on the start's rank or file is one move away. For a knight the map is surprising: some near squares take more moves than farther ones, because the knight cannot make small adjustments.