Let's visualize squares partially before visualizing a 8 x 8 grid.
It is the visualization of a 2 x 2 grid.
a 4 x 4 grid
the top half board
the bottom half board
the kingside
the queenside
the center 16 squares
Below is the basic visualization of a 8 x 8 grid. A 2 x 2 grid as a unit gives us a view of a 4 x 4 grid.
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