Many solutions down there ! Here's one which is not the first one you might think of. Adding another equilateral triangle and using a 60° rotation. #MathGIF
For the colorblind folks, here's the black & white version as published in the AMS Calendar by @evelynjlamb.
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This pattern is much bigger than I thought, (1st room). Two sizes, on one wall the rectangles have the size of a brick. I noticed it's just a small change in the rectangle&square pattern, common on the andalusian floors, also in this room. #Alhambra 2/n
How do you see these points moving ?
Ben Sparks @SparksMaths started a great talk last week for #latemaths with this simple animation. People see different things. What do *you* see ?
Some see the endpoints of a twirling baton as @shskaercher mentioned it.
And Mark even pictured the trace of this baton whose envelope is an astroid.