Lissajouskurva

Question book-4.svg
Författare/Upphovsman: Tkgd2007, Licens: CC BY-SA 3.0
A new incarnation of Image:Question_book-3.svg, which was uploaded by user AzaToth. This file is available on the English version of Wikipedia under the filename en:Image:Question book-new.svg

Lissajous curve 3by4.svg
Författare/Upphovsman: Alessio Damato, Licens: CC BY-SA 3.0

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

and then I post-processed with Inkscape

Lissajous curve 3by2.svg
Författare/Upphovsman: Alessio Damato, Licens: CC BY-SA 3.0

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

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

with ${\displaystyle a=3}$, ${\displaystyle b=2}$ and ${\displaystyle \delta =\pi /2}$.

Lissajous-Figur 1 zu 3 (Oszilloskop).jpg
Författare/Upphovsman: unknown, Licens: CC BY-SA 3.0

Lissajous curve 1by2.svg
Författare/Upphovsman: Alessio Damato, Licens: CC BY-SA 3.0

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

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

with ${\displaystyle a=1}$, ${\displaystyle b=2}$ and ${\displaystyle \delta =\pi /2}$. I created it with the following GNUplot code:

set samples 5000
set terminal svg
set output "Lissajous_curve_1by2.svg"
# plotting within a square
set size square

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

# plot
set parametric
a=1
b=2
delta=pi/2
plot [0:2*pi] sin(a*t + delta),sin(b*t) with lines linewidth 2

and then I post-processed with Inkscape

3D Lissajous figure (9, 4, 1).jpg

Lissajous curve 5by4.svg
Författare/Upphovsman: Alessio Damato, Licens: CC BY-SA 3.0

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

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

with ${\displaystyle a=5}$, ${\displaystyle b=4}$ and ${\displaystyle \delta =\pi /2}$. I created it with the following GNUplot code:

set samples 5000
set terminal svg
set output "Lissajous_curve_5by4.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=5
b=4
delta=pi/2
plot [0:2*pi] sin(a*t + delta),sin(b*t) with lines linewidth 2

and then I post-processed with Inkscape

Lissajous phase.png
Författare/Upphovsman: TedPavlic, Licens: CC BY-SA 3.0
Figure showing several Lissajous figures for different phase delays.

Lissajous curve 7by6.svg
A Lissajous curve that can be expressed in parametric form as:

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

with ${\displaystyle a=7}$, ${\displaystyle b=6}$ and ${\displaystyle \delta =\pi /2}$. I created it with the following GNUplot code:

set samples 5000
set terminal svg
set output "Lissajous_curve_1by2.svg"

# plotting within a square
set size square

# remove most of information from the picture
unset xtic
unset ytic
set key off

# plot
set parametric
a=7
b=6
delta=pi/2
plot [0:pi/2] sin(a*t + delta),sin(b*t) with lines linewidth 2

and then I post-processed with Inkscape: I converted the graph to beziers (aka Simplify), cloned and rotated the curve (π/2) to get the entire graph (2π), and resized the final image to 600x600 with a 18.854px margin, like the others. I also manually edited and removed any unnecessary elements. All of this resulted in a smoother graph with a small file size.

Lissajous curve 5by6.svg
Författare/Upphovsman: Alessio Damato, Licens: CC BY-SA 3.0

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

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

with ${\displaystyle a=5}$, ${\displaystyle b=6}$ and ${\displaystyle \delta =\pi /2}$. I created it with the following GNUplot code:

set samples 5000
set terminal svg
set output "Lissajous_curve_5by6.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=5
b=6
delta=pi/2
plot [0:2*pi] sin(a*t + delta),sin(b*t) with lines linewidth 2

and then I post-processed with Inkscape