Editing Lissajous curve (section)

==Examples==
[[File:Lissajous animation.gif|thumb|upright=3.1|Animation showing curve adaptation as the ratio {{math|{{sfrac|''a''|''b''}}}} increases from 0 to 1]]

The animation shows the curve adaptation with continuously increasing {{math|{{sfrac|''a''|''b''}}}} fraction from 0 to 1 in steps of 0.01 ({{math|1=''δ'' = 0}}).

Below are examples of Lissajous figures with an odd [[natural number]] {{math|''a''}}, an even [[natural number]] {{math|''b''}}, and {{math|1={{abs|''a'' − ''b''}} = 1}}.

<gallery>
File:Lissajous curve 1by2.svg|{{math|1=''δ'' = {{sfrac|''π''|2}}}}, {{math|1=''a'' = 1}}, {{math|1=''b'' = 2}} (1:2)
File:Lissajous curve 3by2.svg|{{math|1=''δ'' = {{sfrac|''π''|2}}}}, {{math|1=''a'' = 3}}, {{math|1=''b'' = 2}} (3:2)
File:Lissajous curve 3by4.svg|{{math|1=''δ'' = {{sfrac|''π''|2}}}}, {{math|1=''a'' = 3}}, {{math|1=''b'' = 4}} (3:4)
File:Lissajous curve 5by4.svg|{{math|1=''δ'' = {{sfrac|''π''|2}}}}, {{math|1=''a'' = 5}}, {{math|1=''b'' = 4}} (5:4)
File:Lissajous relaciones.png|Lissajous figures: various frequency relations and phase differences Aesthetically interesting Lissajous curves with a finite sum of the first 100, 1000 and 5000 prime  number frequencies  were calculated.
</gallery>