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Are those "rays" physical or caused by timezones?
Remember that the world is tilted as it rotates. The "rays" are from the earth's rotation at an angle changing the sundown time on an axis.
Also the Mercator projection is infamously inaccurate. I'm surprised the straight lines are straight, actually.
This is absolutely not Mercator (otherwise, meridians would be all vertical and the Polar Circle a straight horizontal boundary), and the diagonal lines do not quite appear straight.
The timezones are the thick grey lines on the map, and you can see they are causing breaks in the "rays".
I'm not sure what's causing the rays.
Going south makes the earliest sunset happen later (because every sunset happens at the same time at the equator) and going west within a timezone makes it happen later too (since the sunset moves from east to west). Put those together and you get the diagonals.
They're caused by how the data is split on the half hour. +-1min changes color drastically.