Note

This Mathematica notebook is from the WWW project A Visual Dictionary of Special Plane Curves. Copyright © 1995-2000 by Xah Lee. (http://xahlee.org/)

Packages and Initializations

animation of r==Sin[n*t] with variable n.

This animation blow show r == Sin[n t] with n going from 2 to 3. It shows what happens when n is irrational and how a 4 leafed rose transforms to a 3 leafed rose smoothly.

Do[
        ParametricPlot[Sin[n t] {Cos[t], Sin[t]}, {t, 0, 5 π}, 
          PlotLabel -> 
            StringForm["r == Sin[`` t]", PaddedForm[N@n, {3, 2}]], 
          PlotStyle -> {Hue[0]}, 
          Ticks -> {{-1, - .5,  .5, 1}, {-1, - .5,  .5, 
                1}}, PlotRange -> {{-1, 1}, {-1, 1}}, 
          AspectRatio -> 1], {n, 2, 3, (1/50)}];