One generalization of this concept I see is: Instead of having a sequence of successive states, you only need the initial state and a function telling you how to compute the next state from previous one.

You can also see a connection to a version control system like Git. Instead of keeping snapshots of all the contents of the repository after each commit, one can keep only the initial repository state and changes in each commit. Then to get to N-th state you say "Apply first N commits to the initial state".

In the bouncing DVD logo example the "function to compute next state" or "commit contents" is just easy and regular, to the point of being expressible via simple math functions.

This is also known as Event Sourcing.