Note

This Mathematica notebook is from the WWW project A Visual Dictionary of Special Plane Curves. Copyright © 2004 by Xah Lee. (http://xahlee.org/)

Lissajous curve

The following generate a graphic of representative varieties of lissajous.

lissajous = 
        Table[pp[{1/GoldenRatio*Sin[b*t*(2*Pi) + c], 
              Sin[t*(2*Pi)]}, {t, 0, LCM[1/b, 1]}, 
            AspectRatio -> Automatic, DisplayFunction -> Identity, 
            PlotRange -> {{-1, 1} 1/GoldenRatio, {-1, 1}}, 
            Axes -> True, PlotStyle -> Hue[0], PlotPoints -> 100, 
            Ticks -> None, 
            Epilog -> Text[
                StringForm["`1`,`2`", b, c], { .5, -1}]], {c, 0, 1, 
            1/4}, {b, 1, 2, 1/5}];

Show[GraphicsArray[lissajous /. pp -> ParametricPlot]]

?BowditchCurve

ParametricPlot[ 
      Evaluate@BowditchCurve[3/5, Pi][t], {t, 0,  10 Pi}]