I'm not an expert, but think about linear algebra.

you can write each dimension value in terms of time t(a) -> t(b)

x = sin(t) y = 2cos(t)

or whatever. if there is a symmetry, one of those equations should cancel out.

another way to look at it is, if you can always get x, and know y "for free", or the other way around, then x and y aren't really independent. there's some other thing, like sqrt(t) that's generating both values.