Each of the white circles are really just moving back and...

intothecontinuum:

Each of the white circles are really just moving back and forth along a straight line. The second animation shows the same exact motion, but with straight lines added to make the linear motion obvious. Inspired by the Tusi-couple.

Mathematica code:

Manipulate[ Graphics[ {{Black, Disk[{0, 0}, 1.05]}, Table[ {White, Opacity[o], Line[ Table[1.05 s {Cos[n2 Pi/m], Sin[n2 Pi/m]}, {s, -1, 1, 2}]]}, {n, 1, m, 1}], Table[ {White, Disk[ Cos[2 Pi (t + n/m)] {Cos[n2 Pi/m], Sin[n2 Pi/m]}, .05]}, {n, 1, m, 1}]}, PlotRange -> 1.1, ImageSize -> 500], {{m, 16}, 1, 20, 1}, {{o, .5}, 1, 0}, {t, 0, 1}]

Very cool and counterintuitive how interactions of circles produce perfectly straight lines...

Albegraic!