Harmonograph

x[A1_, A2_, f1_, f2_, p1_, p2_, d1_, d2_, t_] := A1 Sin[t f1 + p1] E^(-d1 t) + A2 Sin[t f2 + p2] E^(-d2 t)
y[A3_, A4_, f3_, f4_, p3_, p4_, d3_, d4_, t_] := A3 Sin[t f3 + p3] E^(-d3 t) + A4 Sin[t f4 + p4] E^(-d4 t)
 
 
Manipulate[
 ParametricPlot[
  {x[A1, A2, f1, f2, p1, p2, d1, d2, t],
   y[A3, A4, f3, f4, p3, p4, d3, d4, t]},
  {t, 0, tmax},
  PlotPoints -> 200, Axes -> False, PlotStyle -> {Thick, Opacity[0.5]}, PlotRange -> All
 ],
 Style["time", Bold, Medium],
    {{tmax, 100}, 0.001, 200},
 Delimiter,
 Style["x1", Bold, Medium],
    {{A1, 1}, 0, 4},
    {{f1, 1}, 0, 20, 0.5, Appearance -> "Open"},
    {{p1, 0}, 0, 2 Pi},
    {{d1, 0.01}, 0, 0.1},
 Delimiter,
 Style["x2", Bold, Medium],
    {{A2, 1}, 0, 4},
    {{f2, 2}, 0, 20, 0.5, Appearance -> "Open"},
    {{p2, 0}, 0, 2 Pi},
    {{d2, 0.01}, 0, 0.1},
 Delimiter,
 Style["y1", Bold, Medium],
    {{A3, 1}, 0, 4},
    {{f3, 3}, 0, 20, 0.5, Appearance -> "Open"},
    {{p3, 0}, 0, 2 Pi},
    {{d3, 0.01}, 0, 0.1},
 Delimiter,
 Style["y2", Bold, Medium],
    {{A4, 1}, 0, 4},
    {{f4, 4}, 0, 20, 0.5, Appearance -> "Open"},
    {{p4, 0}, 0, 2 Pi},
    {{d4, 0.01}, 0, 0.1},
  ControlPlacement -> Left
]