Picturesque Parametrics

Yes, parametric equations can be beautiful! Well, the graphs produced by them can be anyway. Take the Lissajous Equations for example, a pair of simple trigonometric parametric equations, that produce an infinite amount of stunning, alluring and varied graphs, simply by changing two or three variables within the formulae.

Take a look at some of the graphs below, surely worthy candidates to be called "art"? 

 So how were these graphs created? Simple parametric equations!

x=sin(At+B)cos(Ct)

y=sin(At+B)sin(Ct)

by changing the variables A, B and C, we can produce the most magnificent and elegant of shapes and patterns. The graphs above were made using A=96 B=3 C=1, A=100 B=7 C=427, A=36 B=1 C=173 and A=46 B=22 C=173.

You can try some of these out for yourself using Excel, which is how I made these graphs.

These ones used A=7 B=5 C=80, A=7 B=1 C=93, A=76 B=11 C=57 and A=55 B=3 C=189. And here are some more:

and these used A=51 B=1 C=50, A=36 B=4 C=209, A=87 B=11 C=13 and A=58 B=1 C=475.

I hope you're as fascinated as I am with these graphs, and that it will open you up to the naturally gorgeous world of maths.