I don't know if this is necessarily true or not, but all the mandelbrot set zooming videos seem to end in a picture of concentric circles (since the zoom is so precise, the fractals that have very small details) and a slightly different looking version of the original mandelbrot set or if not just a rotated original mandelbrot set. I'm just curious why do these videos end this way? Is it purely coincidence or is it a property of the final iterate, or does the computation become easier to zoom and stops once it reaches the converging parts of the mandelbrot set? Here is an example picture..
Pretty sure it's an aesthetic choice, as Mark says in his comment. It arguably makes a more satisfying end to end inside a mini copy (or just before). Alternatives are to end outside the set (which would fill the screen with a flat colour eventually), or on the boundary (perhaps spiralling forever into a Misiurewicz point).
With pertubation and series approximation techniques being used for deep zooms, it can be computationally cheaper to reuse the primary reference computations between keyframes, and a central mini copy makes for a good primary reference. But that has to be weighed up against the iteration counts increasing asymptotically more quickly when approaching a mini copy than when approaching a Misiurewicz point, for example. The computation time for the last few keyframes of a video ending at a mini copy can dominate the time taken for the rest of the video.