Million Base is a database of 2.2 million chess games. Steve Tung visualized chess piece journeys based on this data, for each piece on the board. Above is the footprint for the white knight. Each thin line represents 500 moves, and from what looks like a little bit of random noise to offset each line, you see a more prominent path for more frequent hops.
Of course, because of starting points and game rules, there’s a unique pattern for each piece.
Here’s the black queen, which relatively more board coverage than others:
The white king, which is more limited in movement:
In contrast, here’s the black pawn that starts in position b7.
See the paths of all the pieces. [Thanks @networkstudies]