FixedPointList

FixedPointList[f, expr] applies f to expr until UnsameQ applied to the two most recent results returns False. It returns a list of all intermediate results.

Attributes[FixedPointList] := {Protected}

Simple examples

In[1]:= Length[FixedPointList[Function[(Slot[1] + (3)/(Slot[1]))/(2)], 1.]]
Out[1]= 7

In[2]:= FixedPointList[Function[D[Slot[1], x]], x^3]
Out[2]= {x^3, 3*x^2, 6*x, 6, 0, 0}