Discretely delta-hedge a long call along a price path; the replicating portfolio tracks the option value, the residual is the hedge error.
Delta hedging replicates an option by holding delta shares of the stock and a cash position, rebalanced as the price moves. This simulator follows a call option along a simulated stock path and compares the hedging portfolio with the option value, showing the hedge error that remains when you can only rebalance at discrete times.
Delta changes continuously, but a real hedge is only adjusted at discrete times. Between rebalances the option's curvature (gamma) creates a gain or loss that the linear stock position cannot match.
The hedge error shrinks. In the Black–Scholes model, with continuous rebalancing it would vanish, which is exactly the argument that gives the Black–Scholes price.