This Infinite Integral Tower Actually Converges? Sorta...

Check out my MATH MERCH line in collaboration with Beautiful Equations ►https://www.beautifulequation.com/pages/trefor Take some function f(x) and compose it with itself over and over again, f(f(f(f(f.... What is the limit of that sequence? Certainly a converges for fixed points where f(x)=x, and indeed there is a whole theory about fixed point iteration that looks at the stability of fixed point. We've seen this in my previous video on cos(cos(cos(cos(... where the Banach Fixed Point Theorem guaranteed us a convergent sequence no matter where we started. In this video however, I've got a rather funky example, one where the f(x) is a particular integral and it has the golden ratio as a fixed point. However, it has all sorts of interesting dynamics beyond just the fixed points. My t ...