Some fairy chess piece possibilities involving being able to move to a relatively large area. The goal is to lessen the relative weakness of pieces that move in a line as the board area increases quadratically. (Though a piece that moves in a line can reach quadratic area in two moves.)
The piece jumps to any other square on the quarter of the board it currently occupies.
The piece jumps to any square in the rectangle bounded by its current square and the nearest corner. The closer to the center of the board the piece sits, the more powerful it is.
Both of these pieces will need some additional kind of move to escape the quarter or corner of the board they are currently on.
Other possible variations such as color bound, defining the target area by an edge instead of a corner. Can only move to a subset of the target region reachable by some (perhaps unlimited) number of micro steps of certain types. Limiting to two micro steps is a hook move.
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