"Reminds me of way back when, just for fun, I tapped a number into a calculator, then LOG then x2. Repeat forever. I built up a distribution, plotting it on a Tektronix 4051. I might have a brittle old sheet of thermal paper with…"
"I've seen O(n) with log n, of course. I've seen log log n. It comes up in image processing and various algorithms. But I don't recall seeing the triple log come up in practice. Are there any curiously elegant…"
"Yeah, taking absolutes won't do anything useful. Repeating logarithms takes you to wildly unpredictable negative territory, absoluting it and then logarithming again makes for some randomish values, so it's probably a chaotic dynamic…"
"This has me thinking. A long time ago, as an undergrad in physics, I got curious about iterated exponentials, exp_a(x) such that exp_0(x)=x, exp_1(x)=e^x, and exp_a(exp_b(x)) = exp_(a+b)(x) . Is there a "half exponential" function…"