
Follow Through
Put down points at multiples of
$4\pi/11$, with each repeated, and form the resulting star. Then linearly interpolate the
$i$th point with the
$(i+9)$th point.
Here's the code:
smootheststep[t_] := -20 t^7 + 70 t^6 - 84 t^5 + 35 t^4;
DynamicModule[{n = 11, t, cols = RGBColor /@ {"#111F4D", "#F4F4F4"}},
Manipulate[
t = smootheststep[s];
Graphics[{cols[[1]],
Polygon[
(1 - t) # + t RotateLeft[#, n - 2]
&[Riffle[#, #] &[Table[{Cos[θ], Sin[θ]}, {θ, π/2, 4 π + π/2 - 4 π/n, 4 π/n}]]]]},
PlotRange -> Sqrt[2], ImageSize -> 540, Background -> cols[[-1]]],
{s, 0, 1}]
]