Re: Incorrect plotting of Lissajous-figures

• To: mathgroup at smc.vnet.net
• Subject: [mg25919] Re: Incorrect plotting of Lissajous-figures
• From: "Bill Bertram" <wkb at ansto.gov.au>
• Date: Tue, 7 Nov 2000 23:05:04 -0500 (EST)
• Organization: Australian Nuclear Science and Technology Organisation
• References: <8u8dmk\$7dd@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Rene Meyer <rene.meyer at s2000.tu-chemnitz.de> wrote in message
news:8u8dmk\$7dd at smc.vnet.net...
> Hello,
>
> while using Mathematica 4.0.2.0 to plot a Lissajous-figure with
>
> ParametricPlot[{Cos[500t], Cos[500t + Pi/4]}, {t, 0, 2Pi}]
>
> I found that with growing coefficients of t the figure (which should
> be a ellipse with an angle of 45 degrees between its longer main axis and
> the x axis) have the effect of filling up the whole ellipse with
> points. Is this an effect of rounding errors or is this a bug in
> mathematica?

Hi Rene,

This is not a bug. First, why would you want to draw the ellipse 500 times
on the same graph, which is what ParametricPlot with a parameter 500t with
{t,0,2Pi} is trying to do. By using a parameter of 500t instead of t,
successive points for the plot will have a spacing of 500 dt instead of dt
where dt is the default interval used by Mathematica. That is the reason why
your ellipse appears to be filled in.You can reduce the value of 500dt by
using the PlotPoints option eg PlotPoints -> 1000 but why bother!

Cheers,

Bill

```

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