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+--- Thread: Is there any ways to compute iterations of a oscillating function ? (/showthread.php?tid=1779)
Is there any ways to compute iterations of a oscillating function ? - Shanghai46 - 10/14/2023
So we all know we can use fixed point to calculate iterations. Functions that converge to a real value, then using Schroeder's equation to compute it.
But, when the function converges to a oscillating pattern? When the upper limit and downwards limit converges, and it keeps oscillating between the 2 (like for \({^x}a\) when \(a\) is between \(0\) and \(e^{-e}\)), is there a way, an equation to compute it?
The only way I've found to do so, is with function that converge into the negative iterations and oscillates in the positive (or vice versa if you use the inverse function). You compute it on the converging side, then apply the inverse function, but it's kinda cheating...
RE: Is there any ways to compute iterations of a oscillating function ? - Shanghai46 - 10/15/2023
(10/15/2023, 12:47 AM)leon Wrote: The best way is to converge on the function could be using a oscillating diagram or by tetrating the limit and the maximum of the equation until it's over.
Ummmm......What?
RE: Is there any ways to compute iterations of a oscillating function ? - tommy1729 - 10/15/2023
One way is using sin or cos
For instance
https://tetrationforum.org/showthread.php?tid=1622
Bo and Leo and others went into this in various places.
regards
tommy1729
RE: Is there any ways to compute iterations of a oscillating function ? - tommy1729 - 10/15/2023
(10/15/2023, 11:17 PM)tommy1729 Wrote: One way is using sin or cos
For instance
https://tetrationforum.org/showthread.php?tid=1622
Bo and Leo and others went into this in various places.
regards
tommy1729
btw , the links are dead but just paste the (thread identifation numbers) tid numbers and you can get there !
( because the name of the domain changed )
regards
tommy1729