You've seen the boring zoom videos: go towards -2+0i for half the video, then go offcenter and zoom the rest of the way to the miniset.

The boringness can be quantified like this: the set is asymptotically self-similar about Misiurewicz points like the antenna tip. The (complex) multiplier of a Misiurewicz point is the derivative of its periodic cycle (the preperiodic part is ignored). The asymptotic self-similarity means that zooming (and rotating) by the multiplier leaves the image the same, provided you are zoomed far enough, and the colouring is not too dependent on iteration counts (for example, distance estimation works, as does monochrome edge detection of atom domains, I guess binary decomposition would work fine too though I haven't tried it yet). Then when you go off-center you take the square root of the multiplier (or whatever root for other powers) at the doubling point, and square root again at the quadrupling point, etc.

If you align the zoom keyframes just right compared to the multiplier, you end up with repeating loops of keyframes (in general this means spinning, but you can unspin when assembling the zoom video). So you don't need to really render the vast majority of keyframes, you can just render a few and repeat them, splicing the repeating parts together with non-repeating transition sections.

For example, in the Mandelbrot-Burning Ship-Mandelbrot-Mandelbrot hybrid, zooming into the point 0-1i with 2x zoom factor key frames, the first few frames (about 20-30) are unique, but then there is a repeating loop of 10 key frames. You could repeat this loop 160 more times, then go off-center with a transition of 40 frames, arriving at another repeating loop, this time of 5 frames. Repeat this loop 160 times and double up with a transition of 20 frames. The next loop could be 2.5 frames, but to simplify things (avoid changing keyframe interval) you can extend it to 5 frames as before. Repeat it 80 times, and we're already at zoom depth 2^2900 or so with only 100 or so key frames really needing to be rendered.

Howver, this method is not very practical for accelerating rendering of videos anyone would actually want to watch

See also

https://mathr.co.uk/blog/2017-06-06_asymptotic_selfsimilarity.html which just covers zooming into Misiurewicz points, without the transitions when going off-center or doubling.

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