# How to move around an orbit?

Suppose I have a function $$f(x)$$ (for drawing purposes, I will image it to be $$2D$$). Is there some sort of dynamics/set of differential equations etc that allows me to move around the orbit defined by the level set $$f^{-1}(c) = \{x\,:\, f(x) = c\}$$ It would look something like this.