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CODE:
Clear[t, h, range];
h = ParametricPlot[{(t - Sin[t]) 2/3 + RandomReal[]/250,
   0.65 Cos[t] + .9 Sin[t - Sin[t]^2/3] +
    RandomReal[]/150}, {t, - 2 Pi, 2 Pi}, Axes -> False,
  PlotStyle -> Red, PlotPoints -> 250]; range =
First /@ Differences /@ (PlotRange /. Options[h]); Show[h,
AspectRatio -> Last@range/First@range]

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