#long durational

[abramovicinstitute]

Animated GIF (700 x 700) Mathematica code:

F[L_, a_, r_, s_, t_] := Table[ {-(r + s*Cos[t])^n*Sin[n*a], (r + s*Cos[t])^n*Cos[n*a]}, {n, 0, L}]; Manipulate[ Graphics[ Table[ Rotate[ Table[ Translate[ Rotate[ {White, Polygon[F[ 160, Pi/2 + (u + k)*2 Pi/5, .975, 0, 0]]}, u*2 Pi, {0, 0}], 3{Cos[(u + k)*2 Pi/5],Sin[(u + k)*2 Pi/5]}], {k, 0, 4, 1}], j*Pi/5, {0, 0}], {j, 0, 5, 5}], PlotRange -> 4, ImageSize -> 700, Background -> RGBColor[54/255, 70/255, 93/255]], {u, 0, 59/60, 1/60}]

[abramovicinstitute]

This animated GIF is 20 frames long and takes 2 seconds to repeat itself, but if you pick any point and follow its motion continuously it will take 2000 seconds (about 30 minutes) for the point to return to the same location it was in when you started watching it! How long can you follow a single point?

Mathematica code:

G[p_, q_, a_, b_, c_, t_] := Graphics[  Table[   {Opacity[.7], White,    Disk[     {.71*Cos[a (.05*t + n)*Pi/500 + p],      Cos[b (.05*t + n)*Pi/500 + q]},      .002*Cos[c (.05*t + n)*Pi/500] + .005]},   {n, 1, 1000}],  PlotRange -> {{-.715, .715}, {-1.005, 1.005}}, Background-> RGBColor[54/255,70/255,93/255], ImageSize -> 500] Manipulate[   Show[    G[0, .2, 29, 13, 11, t],    G[0, .2, 19, 31, 9, t],    G[.3, .29, 3, 23, 17, t],    G[0, .3, 43, 7, 3, t],    G[.1, .13, 31, 19, 2, t]], {t,1,20,1}]