Random forever. If the digits started to repeat, that means it’s a fraction where you know the numerator and denominator.
BTW here’s an easy but slow formula for approximating it:
pi = 4 x (1/1 - 1/3 + 1/5 - 1/7 ...)
It’s an infinite sequence of fractions, but you never get to a fraction that’s the “last” fraction.
Excellent response. Thanks man!