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The Power of Hexagonal Binning

Capri Granville explains hexagonal binning to us and gives a few examples:

The reason for using hexagons is that it is still pretty simple, and when you rotate the chart by 60 degrees (or a multiple of 60 degrees) you still get the same visualization.  For squares, rotations of 60 degrees don’t work, only multiples of 90 degrees work. Is it possible to find a tessellation such that smaller rotations, say 45 or 30 degrees, leave the chart unchanged? The answer is no. Octogonal tessellations don’t really exist, so the hexagon is an optimum. 

Every time I see one of these, I think of old-timey strategy war games.