Tunnock's Hypnotism

n = 30;
r = 5;
d = 1;
\[Omega] = -1;
Manipulate[
 Show[
  Table[
   ParametricPlot[
    {-d/2 + d/(
      1 + Tan[\[Theta]] Tan[\[Theta] + \[Alpha] + 2 \[Theta]0]),
     d Sin[\[Theta] + \[Alpha] + 2 \[Theta]0]/(
      Cos[\[Theta] + \[Alpha] + 2 \[Theta]0] +
       Tan[\[Theta]] Sin[\[Theta] + \[Alpha] + 2 \[Theta]0])},


    {\[Theta], 0, Pi},
    PlotStyle -> Directive[Opacity[1], Thick, RGBColor[0.5, 0, 0.1]],
    PlotRange -> 2, Axes -> None]
   , {\[Alpha], -2, 2, 2 Pi/n}],
  Graphics[
   {RGBColor[0.7, 0.1, 0.1], Opacity[0.8],
    Table[
     Polygon[{{-d/2, 0}, {-d/2, 0} +
        r {Cos[\[Theta] + \[Theta]0], Sin[\[Theta] + \[Theta]0]}, {-d/
          2, 0} + r {Cos[\[Theta] + Pi/n + \[Theta]0],
          Sin[\[Theta] + Pi/n + \[Theta]0]}}]
     , {\[Theta], 0, 2 Pi, 2 Pi/n}],
    Table[
     Polygon[{{d/2, 0}, {d/2, 0} +
        r {Cos[\[Theta] + \[Omega] \[Theta]0],
          Sin[\[Theta] + \[Omega] \[Theta]0]}, {d/2, 0} +
        r {Cos[\[Theta] + Pi/n + \[Omega] \[Theta]0],
          Sin[\[Theta] + Pi/n + \[Omega] \[Theta]0]}}]
     , {\[Theta], 0, 2 Pi, 2 Pi/n}],
    {Opacity[1], White, Disk[{d/2, 0}, 0.2], Disk[{-d/2, 0}, 0.2]}
    }
   , PlotRange -> 2]
  ]
 ,
 {\[Theta]0, 0, 2 Pi/n}]