File:Lissajous curve 3by4.svg

A Lissajous curve, that can be expressed in parametric form as:

${\displaystyle x=A\sin(at+\delta ),\quad y=B\sin(bt)}$

with ${\displaystyle a=3}$, ${\displaystyle b=4}$ and ${\displaystyle \delta =\pi /2}$. I created it with the following GNUplot code:

set samples 5000
set terminal svg
set output "Lissajous_curve_3by4.svg"

# plotting within a square
set size square

# remove most of information from the picture
set noxtic
set noytic
set key off

# plot
set parametric
a=3
b=4
delta=pi/2
plot [0:2*pi] sin(a*t + delta),sin(b*t) with lines linewidth 2