Your "simulation" might not need state
The author gave just a simple example, the DVD animation, but it is much more than this,  this technique is the industry standard in game art for all the background animations of a game, like the wind blowing the leaves and the grass, the water waving and foaming. Those effects are often implemented in shaders, and state in GPU shaders is something very very expensive, so they are implemented as a function of time (often based on a noise function to give a more natural feel).One important thing to note is that is not about eliminating all state (that would be absurd after-all a game is all about the state of the main character), but crucially to never take the `t - 1` state of the thing being animated. In games for example, a function animating a blade of grass may take into account many parts of the game state, they often take the character position as a multiplier to amplify the movement if the character is close, imitating collision with the character without actually having to calculate collisions.