"I'm still unsure what the term 'animated' means in this context. Rocketnia?"
For the benefit of people here, this is what David Barbour had to say over email to akkartik and myself:
"Animated term rewriting means that the term is changing over predictable time, in a predictable manner - i.e. you could literally set up a viewer and watch the term change in real-time. If the term specified something like which jpeg image to display, or how to position a robot, this could easily be lifted to visual or physical animations. Animation, in general, is about controlling an external system over time."
I think the benefit here isn't (only) the ability to express animation, but (also) the ability to use a divergence-capable term rewrite system in a way that isn't the end of the world when the system actually does diverge.
