Crowds and I

Let \(f\) denote the density function of a crowd in a given space \(X\), and let \(\nabla f\) denote the gradient vector field. If I am at a given point \(x\in X\), compute the integral curve \(c_{\nabla f}(t)\) such that \(c_{\nabla f}(0)=x\) and \( c_{\nabla f}'(t) = -\nabla f(c_{\nabla f}(t)) \). You just computed the trajectory in which I will move.