Take any map projection and animate a rotation of the earth underneath it. The axis of rotation need not be the physical axis around which the earth actually rotates. Land masses will move around and distort in weird ways.
Pepper the globe with points at a uniform density. Project the points into 2D with a map projection. The points will be scattered in some distribution in 2D. (If it's an equal-area projection, the distribution will be uniform in 2D.) Next, rotate the globe as before. Although the points move around in the projection, their statistical 2D distribution remains the same.
In the rotating sphere script, one does not have to limit to the orthographic projection.
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