Clear[x,y, phi,a , b , c]

phi = 2;
a = 1;
b = 1;
c = 1;

x[t_, phi_] := Sin[a t + phi] * Cos[b t]
y[t_, phi_] := Sin[c t]

ParametricPlot[
    {x[t, phi], y[t, phi]},
    {t, 0, 2 π},
    Axes -> True
  ]

Animate[
  ParametricPlot[
    {x[t, phi], y[t, phi]},
    {t, 0, 2 π},
    PlotStyle -> {Thickness[0.01], ColorData["Rainbow"][Mod[phi, 2 π]/(2 π)]},
    PlotRange -> 2,
    Axes -> False,
    Background -> Black
  ],
  {phi, 0, 2 π},
  AnimationRate -> 0.1,
  AnimationRunning -> True,
  AnimationRepetitions -> ∞
]

frames = Table[
  ParametricPlot[
    {x[t, phi], y[t, phi]},
    {t, 0, 2 π},
    PlotStyle -> {Thickness[0.01], ColorData["Rainbow"][Mod[phi, 2 π]/(2 π)]},
    PlotRange -> 2,
    Axes -> False,
    Background -> Black
  ],
  {phi, 0, 2 π, 2 π/60}
];

Export["ADHD_Trap.gif", frames]
