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I think your image of the contraction capture is off...also I'm not sure I understand the Drop rule.  Can you get the queen before placing the remaining four pawns?  Are captured pieces droppable?

The Big Crunch idea seems to already be in place in terms of the contraction of the board.  An interesting implementation of the Big Rip idea would be to have the board disappear from the inside out rather than contracting:  say the outer edge of the board is determined by the number of pieces placed throughout the game, and the inner edge is determined by the number of captured pieces.  (This assumes captured pieces are dead for good, not switching sides and dropped.  Also, this probably isn't very close to the actual idea of the Big Rip.)

Sorry, but I'm unclear what point you're making about the contraction capture image. Can you elaborate please?

There are 4 drop levels, and each side begins the game on the first level. At this level only Pawns can be dropped. On dropping the fourth Pawn the level for that player advances to the second. On the second level Knights and Bishops can now be dropped as well as Pawns. The third level is reached when the second Knight or Bishop is dropped. Rooks may be dropped at the third level. Dropping a single Rook advances that players drop level to the fourth level. Once the fourth level is reached the Queen may be dropped.

Captured pieces are removed from the game. They cannot re-enter the game by being dropped again.