How to get Lissajous curve like the following gif

Question

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 show

Where are you stuck? Manipulate and ParametricPlot seem to be an obvious way to go, or? — Kuba, Dec 20 '18 at 12:22
Searching for Mathematica Lissajous reveals this Q&A which may be a duplicate. — bobthechemist, Dec 20 '18 at 12:24
i want to form the curve from one point to the final picture like the gif show @ bobthechemist — Number_9527, Dec 20 '18 at 12:32
i don't know how to get the effect like the picture shows(from one point to the final picture)@Kuba♦ — Number_9527, Dec 20 '18 at 12:37
Side note: this GIF is from http://www.matrix67.com/blog/archives/6947 . Then, what have you tried? — xzczd, Dec 20 '18 at 12:42
i just want to know how to generate a curve from one point continuously to the final curve.@xzczd — Number_9527, Dec 20 '18 at 12:47
@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? — xzczd, Dec 20 '18 at 12:57
I'm asking you to show how you tried them, so we can give you pointed advice. — xzczd, Dec 20 '18 at 13:16

score 3 · Answer 1 · answered Dec 20 '18 at 13:14

3

Animate[
ParametricPlot[{Sin[13 t], Sin[18 t]}, {t, 0, tf}],
{tf, 0, 10}]

answered Dec 20 '18 at 13:14

David G. Stork

1 Answers1