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..

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    $\begingroup$ I really think it's just a matter of choice on the part of the person who generated the animation. $\endgroup$ Commented Mar 8, 2017 at 11:06

1 Answer 1


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.


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