Consider the task of selecting a square on a checkerboard, on a touchscreen interface using one's fat fingers. (E.g., chess UI on a smartphone) To select a black square, swipe horizontally between the two white squares to the left and right of the black square. To select a white square, swipe vertically between the two black squares above and below the white square.

The UI can accurately distinguish between a horizontal and vertical swipe, which reduces the uncertainty by one half of which square was attempted to be selected, and a checkerboard pattern keeps the squares corresponding to different swipe directions far apart.

This could be extended to 4 different square types, with 4 different swipe directions and a 4 color "checkerboard" pattern. Need some design that provides a visual aid about which direction to swipe.

Can it be extended to 8 different swipe directions (diagonals)? Diagonals could be used just for the corners. Can it be extended to a hexagonal grid? I think yes, though the patterns of which square (or hex) is which direction is less elegant.

It cannot be straightforwardly extended to higher dimensions. In 3 dimensions, there are 6 different orthogonal swipe directions, but natural checkerboard-like unit cell contains 8 cubes.

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