Just found a funny construction: Usually when you have to apply a function repeatedly (e.g. for a (mathemtaical) fixed point iteration) you do something lik iterate f x0 !! n
for some n
For golfing i tried to avoid iterate and came up with this (which didn't end up to be shorter)
r f=f.f (=join(.))
r(r r)f x0
this applies f 16 times
if we increase r with one more application (r f=f.f.f) then the same applies f 19683 times.
And for r f=f.f.f.f I already get for f=(+1) and x0=0 a stackoverflow :)