Orthogonally directed

For an orthogonal direction $d$, we say a polyomino is "$d$-directed" if every cell of the polyomino can be reached from an anchor cell without going opposite that direction.

For example, the following polyomino is up-directed with the bottom-left cell as an anchor, since every cell in it can be reached from that cell without going down:

Note that the anchor cell is not necessarily unique, as any cell on the bottom row can be used as an anchor cell.