# GIFs ? + !: Moving Dots

What could we discover in the following images!!…

• Plane disc with fixed curves and moving points:

?:   How do the points really move??…

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!:  The curves inside the black disc are 8 identical circles, passing all through the center of the disc and through other 8 special points on the border of the disc. The moving dots are actually the intersection points of the circles and an imaginary line, fixed at the center of the disc, that rotates around this fixed point!!…

Note that the dots seem to move at constant speed on the circles!!…

• Moving points in 2D that look like 3D:

?:  Could you describe the movement of the dots??…

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!:  The bright central dot seems to be a symmetry point! Around it are moving dots. They form patrons! We see as if the dots are moving outwards sometimes on spiral and sometimes on lines, but actually the dots move periodically in a kind of zig-zag movement!!…

• ?: What can we see??…

!: We have at least two ways to see this: One is, the dots are fixed in a circle that rotates inside the black disc! … Or, the dots pendeln on the lines inside the black disc!

• ?:  Which figures do the dots form??…

!:  In this, say 3D animation, we could say that at first, there is one line of dots close to each other, that starts moving like a chain in a helical way, but then the dots moves away from each other, forming three, and somtimes two, different spiral chains, to finally become a single chain, and so on… And recall the shadow of the dots!

• ?: Is the number od dots constant??…

!:  I would say yes!!… But the point is, to look for a personal strategy to prove it.