playing around with rendering the bifurcation diagram of the logistic map x := a x (1 - x). only 128 lines of commented code.
using the two Feigenbaum constants for zoom in 'a' and 'x' and starting the zoom sufficiently deep, 'a' focused on the end of the first period-doubling cascade (and the critical point x=1/2), makes it loop almost perfectly.
there are two "zooms" in the animation, as "zooming once" flips it vertically.
(it would be a perfect loop approaching the limit of infinite zoom depth, but the number of points calculated that contribute to the view is inversely proportional to the height of visible 'x' , so you need to calculate ever more points when zooming deeper, which slows things down)
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