iterate is a common solution:
> :t iterate
iterate :: (a -> a) -> a -> [a]
So, given a function with a domain the same as its range, a -> a, and an initial input a, produce an infinite list of results in the form:
iterate f a --> [a, f(a), f(f(a)), ...]
And you can access the nth element of the list using !!:
iterate f a !! n
NB iterate f a !! 0 == a.