FixedPointList[f, expr] generates a list giving the results of applying f repeatedly, starting with expr, until the results no longer change.
See notes for FixedPoint.
FixedPointList[f, expr] gives expr as the first element of the list it produces.
The last two elements in the list produced by FixedPointList are always the same.
See The Mathematica Book: Section 2.2.2.
See also: NestWhileList, NestList, ComposeList.