How can you have a function on the $x$ and $y$ axis?
I thought graphing functions worked like this: You have a variable on one of the axis, and a function of the variable on the other axis. How can you graph two independent functions of a common variable on the same graph?
You can also have parametric function $(x(t),y(t))$. For instance, the circle is expressed as the following: $$ x(t)=\rho\cos(t), $$ $$ y(t)=\rho\sin(t), $$ $$ t\in[0,2\pi]. $$ And this figure is two dimensional.
This is one other way to interpret the "classical" way to plot a graph, as you wrote in your question.