Trifolium
The animation shows 800 tangent lines to the trifolium as they slowly move around the curve. In order to make it, I first ran PlaneCurveData["Trifolium", "ParametricEquations"] to get the parametrization, which I then rotate to get a vertically-oriented trifolium:
tri[t_] := RotationMatrix[?/6].{-Cos[t] Cos[3 t], -Cos[3 t] Sin[t]};
After that, it’s just a matter of creating the tangent lines with InfiniteLine[] and choosing some colors. Here’s the code:
With[{d = 2 ?/800.},
Manipulate[
Show[
Table[
Graphics[{Thickness[.001], Opacity[.8], Hue[Mod[(s + t)/?, 1]],
InfiniteLine[tri[t + s], tri'[t + s]]},
PlotRange -> {{-1.4, 1.4}, {-1.18125`, 1.61875`}}],
{t, 0., ? - d, d}],
ImageSize -> 540, Background -> GrayLevel[.1]],
{s, 0, d}]
]
