How many squares a piece controls

Each piece controls a different number of squares, and the number depends on where it stands. A rook attacks $14$ squares from anywhere, because its rank and file always reach both edges: its power is flat. A bishop attacks from $7$ (a corner) up to $13$ (the centre), because diagonals shorten near the edge.

The queen is a rook plus a bishop, so its count is the sum of the two. A knight attacks from $2$ (a corner) up to $8$ (the centre). Shading each square with a piece's attack count draws a contour map, and the maps reveal the board's symmetry.