Krzywa Lissajous

Lissajous curve 3by4.svg
Autor: Alessio Damato, Licencja: 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
Autor: Alessio Damato, Licencja: 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 curve 9by8.svg
Autor: Alessio Damato, Licencja: 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 ${\displaystyle a=9}$, ${\displaystyle b=8}$ and ${\displaystyle \delta =\pi /2}$. I created it with the following GNUplot code:

set samples 5000
set terminal svg
set output "Lissajous_curve_9by8.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=9
b=8
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 1by2.svg
Autor: Alessio Damato, Licencja: 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

Urzadzenie optyczne Lissajous.png

Zestaw z kamertonami i zwierciadełkami do obserwowania krzywych Lissajous:

A - lampa

R, S - kamertony

B, C - zwierciadełka

D - promień światła rzutowany na ekran

Lissajous curve 5by4.svg
Autor: Alessio Damato, Licencja: 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 curve 5by6.svg
Autor: Alessio Damato, Licencja: 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