The Double Pendulum is simulated with real physics, indefinitely. Whenever you open the app, the initial conditions are randomly changed slightly to show different outcomes every single time. You may not see the difference immediately, but the changes are real and after some 30 seconds, the pendulum should be entirely different from any other instance. This you can notice by placing two phones running the app, side by side.
Be warned: This simulation has a pleasant effect of making you drowsy. Especially with your favorite melodic music playing in the background.