We all work with formal languages here:

For almost all point-wise combinations of periodic functions, the period of their combination of the least common multiple of their periods. Why? If they have common factors, they count twice in the period and one is excluded.

Let t = x/2pi

sin(12t) + sin(2t) will have the following period

lcm(12,2) =

lcm(2*2*3, 2) =

2*2*3 =

12

sin(3t) + sin(7t) will have the following period

lcm(13,7) =

lcm(13, 2) =

3*7 =

21

You don’t need primes. You need coprimes. For instance 12 is coprime to 5

sin(12t) + sin(5t) will have the following period

lcm(12,5) =

lcm(2*2*3, 5) =

2*2*3*5 =

60

I was trained as a computational biologist, and while is awesome that evolution reared it’s lovely head in cicada mating, the principle is one of maximizing the period of multiple period functions. Given a choice, you do that by choosing a function with no common divisors. Not knowing the other functions, you do that by choosing a relatively large prime, which will be the smallest number that will not share divisors. products of primes (which aren’t prime) work fine, but they are mch larger.

That’s the theory. Coprimes all the way, if you can choose your repeating pattern set.

]]>(Also, Norcross, apologies for the redaction. I still worry about people who visit from workplaces that run content-filter proxies, so I chose to take the redact-and-publish route rather than dump the comment entirely.)

]]>This is just wonderful.

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