I have invented "anti-runners" as an experiment in piece values; an anti-runner jumps as far away as an unlimited runner could go, then runs back towards itself. Despite their origin, they seem to be interesting pieces on the board in real games.
Things get interesting when the anti-runner is not allowed to run more than a few squares. Thus, an AntiRook3 on an empty board could move from f1 to f8, f7, or f6; to a1, b1, or c1; or to h1 or g1 (but not back to f1, which would be a null-move).
Phrased differently, an "Anti-Rook-One" can only make the longest move a Rook could make; and Anti-Rook-2 can make the longest or the next-to-longest move a Rook could make; and so on.
The theoretical interest is that the Anti-Rook moves to the same distance as a Rook, in the same number of directions, but has less mobility; in other words, a piece that I hope might display the effects of different mobility on piece values uncontaminated by other factors that affect piece values.
Therefore, the Anti-R3's value compared to the R3's value should give a clue about the importance of distance.