this post was submitted on 23 May 2025
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My favorite reference for what youve just described is 3blue1browns Binary, Hanoi, and sierpinski which is both fascinating and super acessable for the average non-nerd.
The pressing point is that this recursive method of counting isn't just a good way of doing it, but basically the most efficient way that it can be done. There are no simpler or more efficient ways of counting.
This allows the same 'steps' to show up in other unexpected areas that ask questions about the most efficient process to do a thing. This allows you to map the same binary counting pattern across both infinite paths of fractal geometry with sierpinskis arrowhead curve and solve logic problems like towers of Hanoi stacking. Its wild to think that on some abstract level these are all more or less equal processes.