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[n*2 Pi/m], Sin[n*2 Pi/m]}, {s, -1, 1, 2}]]},

{n, 1, m, 1}],

Table[

{White,

Disk[

Cos[2 Pi (t + n/m)] {Cos[n*2 Pi/m], Sin[n*2 Pi/m]}, .05]},

{n, 1, m, 1}]},

PlotRange -> 1.1, ImageSize -> 500],

{{m, 16}, 1, 20, 1},

{{o, .5}, 1, 0},

{t, 0, 1}]