File:Lissajous curve 3by2.svg

Summary

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

Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): <semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>x</mi><mo>=</mo><mi>A</mi><mi>sin</mi><mo>⁡<!-- &#8289; --></mo><mo stretchy="false">(</mo><mi>a</mi><mi>t</mi><mo>+</mo><mi>δ<!-- &delta; --></mi><mo stretchy="false">)</mo><mo>,</mo><mspace width="1em"></mspace><mi>y</mi><mo>=</mo><mi>B</mi><mi>sin</mi><mo>⁡<!-- &#8289; --></mo><mo stretchy="false">(</mo><mi>b</mi><mi>t</mi><mo stretchy="false">)</mo></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle x=A\sin(at+\delta ),\quad y=B\sin(bt)}</annotation></semantics> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b9efe37aae3e167657e1b0c03bedb58b5cf7e57" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:33.686ex; height:2.843ex;" alt="{\displaystyle x=A\sin(at+\delta ),\quad y=B\sin(bt)}">

with Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): <semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>a</mi><mo>=</mo><mn>3</mn></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle a=3}</annotation></semantics> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2a0be4b8203e824561fa22ea831a2d86f2f028c9" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:5.522ex; height:2.176ex;" alt="{\displaystyle a=3}">, Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): <semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>b</mi><mo>=</mo><mn>2</mn></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle b=2}</annotation></semantics> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32584049ed5f72969777f89d69b74ee462875e82" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.338ex; width:5.29ex; height:2.176ex;" alt="{\displaystyle b=2}"> and Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): <semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>δ<!-- &delta; --></mi><mo>=</mo><mi>π<!-- &pi; --></mi><mrow class="MJX-TeXAtom-ORD"><mo>/</mo></mrow><mn>2</mn></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \delta =\pi /2}</annotation></semantics> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d58cf73c22f3b86529a7f0234780ae2cf03a363" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:7.856ex; height:2.843ex;" alt="{\displaystyle \delta =\pi /2}">. I created it with the following GNUplot code:

set samples 5000
set terminal svg
set output "Lissajous_curve_3by2.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=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

Licensing

Lua error in package.lua at line 80: module 'strict' not found.