Reversal

Continuing a theme, but now with negative curvature.

Here's the code for the corresponding Manipulate:

Manipulate[Module[{xstep, ystep, cols, curvestyle, n},
  xstep = 1/5;
  ystep = 1/5;
  cols = RGBColor /@ {"#F06161", "#7A3476"};
  curvestyle = Directive[Thickness[.005], cols[[1]]];
  n = 3/2 - Cos[t]/2;
  Show[ParametricPlot[
    Evaluate@
     Table[{(-1)^i r n Cos[?/n], 
        r n Sin[?/n]} /. {? -> ArcTan[x, y], 
        r -> Sqrt[x^2 + y^2]}, {x, -1, 1, xstep}, {i, 0, 1}], {y, 0, 
     1}, PlotRange -> 10/3, Axes -> False, ImageSize -> 540, 
    PlotStyle -> curvestyle, Background -> cols[[2]]], 
   ParametricPlot[
    Evaluate@
     Table[{(-1)^i r n Cos[?/n], 
        r n Sin[?/n]} /. {? -> ArcTan[x, y], 
        r -> Sqrt[x^2 + y^2]}, {x, -1, 1, xstep}, {i, 0, 
       1}], {y, -1, -.0001}, PlotStyle -> curvestyle], 
   ParametricPlot[
    Evaluate@
     Table[{(-1)^i r n Cos[?/n], 
        r n Sin[?/n]} /. {? -> ArcTan[x, y], 
        r -> Sqrt[x^2 + y^2]}, {y, 
       Append[Range[-1, 1, ystep], -.0001]}, {i, 0, 1}], {x, -1, 1}, 
    PlotStyle -> curvestyle]]
  ], {t, 0, ?}]