What would produce tetration in physics?

In a parallel universe much of the physics equation have tetration in them. There are things such as tetrational growth as well as tetrational decay. $x^x$ and $x^{x^x}$ are also found in some physics equations. Super logs and super roots are also necessary for understanding some of the physics of this universe.

What would produce tetration in physics? How would a universe with tetration involved in physics be different from our universe?

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What would produce tetration in physics?

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