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This question already has an answer here:

parameter equation $x= \sin(m t)$, $y= \sin (nt)$,(fix $m=13$, $n=18$ not to change)

I need the picture show the generation of the curve.(start from one point to the final curve like you draw it manually )

In fact,I just want to know how to generate a curve continuously like the gif showenter image description here

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marked as duplicate by corey979, m_goldberg plotting Dec 20 '18 at 19:09

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ Where are you stuck? Manipulate and ParametricPlot seem to be an obvious way to go, or? $\endgroup$ – Kuba♦ Dec 20 '18 at 12:22
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    $\begingroup$ Searching for Mathematica Lissajous reveals this Q&A which may be a duplicate. $\endgroup$ – bobthechemist Dec 20 '18 at 12:24
  • $\begingroup$ i want to form the curve from one point to the final picture like the gif show @ bobthechemist $\endgroup$ – Number_9527 Dec 20 '18 at 12:32
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    $\begingroup$ @kuba has mentioned the necessary function for making the animation, and coding this in Mathematica is straightforward. As I've asked in my last comment, what have you tried? $\endgroup$ – xzczd Dec 20 '18 at 12:57
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    $\begingroup$ I'm asking you to show how you tried them, so we can give you pointed advice. $\endgroup$ – xzczd Dec 20 '18 at 13:16
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Animate[
ParametricPlot[{Sin[13 t], Sin[18 t]}, {t, 0, tf}],
{tf, 0, 10}]
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