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My favorite self-replicating function is the sine, and I spent some time finding it using just its very strong self-replication properties here:

https://myownfortune.wordpress.com/2017/09/21/why-sine-wave/

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By the way, this is a nice article, but you unfortunately mix up "frequency" and "period" in your quantitative discussion. (A function that repeats every 50 units, for example, has a period of 50 units, as opposed to a frequency of 1/50 1/units.)

Yes - what a great question to explore! Nice article, thanks.

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