This page documents some ways in which the Haskell prelude function iterate can be implemented.
First, the direct recursive way seen in the Haskell report:
iterate f x = x : iterate f (f x)
We can also write it in terms of scanl or scanl1 and repeat:
iterate f x = scanl f x (repeat x)
iterate f x = scanl1 f (repeat x)
Or in terms of fix:
iterate f x = fix ((x:) . map f)