I'm writing an advanced interface, but I don't yet have a concept of derivatives or integrals, and I don't have an easy way to construct infinite many functions (which could effectively delay or tween their frame's contributing distance [difference between B and A] over the next few frames).
I can store values for a frame, and I can also consume them or previous values and map into A.
For example, each frame could calculate the distance between B and A, then add that distance to A, but they would be perfectly in sync.
I can keep track of the last N frames' distances and constantly shift old distances off, but this would create a delay, not an elastic effect. Somehow, the function that's popping off past-frames' distances needs to adjust for how long it's been for those 10 frames.
Is there any function I can rewrite each frame, which picks up the progress from it's predecessor, and contributes it's correct delta amount, adjusting for the new total distance between B and A?
Does this question make sense? How can I achieve behavior where A is constantly catching up to B in a non-linear, exponential way?