Originally published at: I am mesmerized by these dots moving around geometric shapes | Boing Boing
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I’m that way with motorcycle racing, just can’t me enough.
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Math: “Hey Physics! I just figured out another way to mess with Humans.”
Physics: “Do tell.”
Math: “12 concentric shapes, all sides with the same length, with dots going around the same speed.”
Physics: “Dude… you’re evil… I love it!”
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Well I started out enjoying it, but then noticed that the inner triangle overlaps the square, and that’s just wrong, and now I can’t bear to look at it at all…
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I’m assuming this works as it does because all those line segments are the same length?
the dots are moving at different speeds: the periods are carefully calculated to give an “all lined up” moment for every one revolution of the outside dot. if they moved at the same speed then the going in and out of phase effect would still happen but take much, much longer.
also, inside triangle misplaced, tsk!
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The dots are not going around at the same speed. Comparing frame 1 with frame 6, it is easy to see that they are set at arbitrary speeds with the octagon and nonagon dots being the fastest and the pentadecagon dot being the slowest. On the attached image, you will see an overlap of frames 1 and 6 (black dots are from frame 6 and light gray dots are from frame 1).
All polygons were created from the same center, shown on the attachment as a printing registration mark.
Edit to add: The whole animation has 800 frames of 0.02 seconds each, for a total of 16 seconds; it is fairly easy to calculate the speed for each dot.
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But it’s displeasing. The top vertex of the triangle should touch the line. Really.
Harmonic resonance has been abused to the point of meaninglessness by the new agers… yet it remains a very cool phenomenon.
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If so, then someone else could say “the triangle is not centered in relation to all other polygons”; it would be impossible to please everybody. 
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That person would be wrong.
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But all polygons have a well established center; including triangles. Clearly, the animator wanted to have thirteen centered polygons; the overlap that some viewers find displeasing is just a side effect to the animator’s desire to maintain the same segment length for all centered polygons.
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Actually, it takes TWO revolution s of the outer dot to return to the initial state. The first revolution results in two lines while the second returns to a single line at the bottom.
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aww, man…no gifs in profile pics?
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There’s a neat program that lets you make music like this, have played with it a bit & found it surprisingly intuitive to use for producing non-grid like patterns :
(linking to that early vid because the main site, while more current - is kind info-overload)
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Imagine the triangle rotating within that square. You’d see the same point just outside the square every 90 degrees of triangle rotation. Your issue is not with the relative position of them but the relative lengths of their sides.
Looks like Discourse disabled that feature (if it was ever an option here)
What I find amazing is how it repeats reliably for the first 100 iterations but then does that totally unexpected other thing …
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This is very much like the patterns you see with video feedback - as you rotate the camera, the various light “dots” align to make either a two, three, four, etc. armed pattern. You gotta watch out for the four-armed one, they can tend to make a nasty symbol (and, although, coincidentally, I was at OU around the same time, and I’m way into video feedback, this linked story is not about me).
Here’s some three, and many-armed feedback of mine:
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It’s even crazier what it does after 1000 iterations…
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