So, when the stone hits another object on it’s ill-fated roll down the hill, there’s always some error with respect to how/where it hits. Chaos theory attempts to describe how quickly trajectories diverge using “Lyapunov exponents“. But still, regardless of the initial condition, the values of x n still settle into the same set or values (same “trajectory”). When you pick two initial values close to each other, they stay close for a while, but soon end up bouncing between completely unrelated values (their trajectories diverge, exponentially). Long story short, chaos theory is the study of how long you should trust what your computer simulations say before you should start ignoring them.