Lissajous Figures

Definition: In mathematics, a Lissajous curve , also known as Lissajous figure or Bowditch curve, is the graph of a system of parametric equations.

x=A\sin(at+\delta),\quad y=B\sin(bt),

definition and equation credits to the wikipedia page http://en.wikipedia.org/wiki/Lissajous_curve

       

The figure is sensitive to the ratio of a and b.

I have made a small change. Instead of a continuous line, I have taken points at regular intervals and joined them. For certain numbers of “a” and “b”, some interesting shapes were seen. I have attached some of them below.

Lissajous Magic 1

Lissajous Magic 6

Lissajous Magic 5

Lissajous Magic 3 Lissajous Magic 4Lissajous Magic 2

It took some time and luck  to arrive at these, so I cannot publish the equations here.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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