I saw this question which had a similar viewpoint, but was limited to straight lines and polynomials. Now we know that we can graph some pretty crazy stuff with parametric equations. For example: 
and even
So naturally one would think that, if we put pen to paper, and drew something, anything, there would be a set of parametric equations to describe that shape or figure (of course, I'm not saying that finding the equations will be easy, but they should exist). So, is this true?