I have 2 functions X(x,y) and Y(x,y) which when given a coordinate pair (x,y) give a new coordinate pair's x, and y components respectively. For instance, given coordinate "(1,2)", "(X(1,2), Y(1,2))" would return "(6,4)". Then, putting that (6,4) into X and Y will give another new point.
Recursively running piece of code that looks like this (x,y) -> (X(x,y), Y(x,y)) makes the point (x,y) move in a smooth path that seems like it can be defined as a parametric equation where you can just plug in some value of "t" and get a point/path, instead of having to run the function a bunch of times.
Is it possible to find this function given any X(x,y) and Y(x,y)? Also, would the result be a parametric equation or is my vocabulary incorrect?
If this is not possible in the general X,Y case, the X and Y I'm actually using is when X is the partial derivative with respect to x of a bigger 3d function F(x,y), and Y is its partial derivative with respect to Y. Here is the actual graph I'm using for this, move the point around press the play button at the top of the graph to see how it moves; that's what I want to describe the path of with a parametric equation: https://www.desmos.com/calculator/5auda9u2fl