This applet attempts to help the viewer see/imagine parametrized surfaces in Eucldiean 4-space. To do so, the applet shows 4 screens - one for each of the four projections from R4 into one of the four coordinate 3-spaces. Each projection is a surface in R3.
In this particular demo, the initial parametric functions have x1(u,v)=u and x2(u,v)=v. Keeping these, regardless of x3(u,v) and x4(u,v), we obtain the function graph of a function f:R2 -> R2.