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1679 in a hexagonal pattern?

Daecon
in Mathematics

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I was reading about the Arecibo message thingy, with the message being transmitted in 1679 bits because there's only two ways to lay out 1679 in a grid, one of which would make "sense" and one that wouldn't.

 

Then I thought, this would only work if aliens used a square grid system (where information can have x & y co-ordinates) for their layouts, which there's no guarantee they would...

 

What if alien visual representations or data were laid out on a hex grid?

 

Maybe they would arrange them from the center spiraling outwards either clockwise or counter-clockwise. Maybe they would be arranged in rows and zigzag columns, or columns and zigzag rows, or maybe they'd be arranged diagonally instead...

 

How would a pattern of 1679 light and dark hexagonals look?

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