• ← FixedPoint
• → Fold

FixedPointList

WMA link

FixedPointList[f, expr]

starting with expr, iteratively applies f until the result no longer changes, and returns a list of all intermediate results.

FixedPointList[f, expr, n]

performs at most n iterations.

• • FixedPointList[Cos, 1.0, 4]

Observe the convergence of Newton's method for approximating square roots:

• • newton[n_] := FixedPointList[.5(# + n/#) &, 1.];

• • newton[9]

Compute the Hailstone Number: for 14:

• • collatz[1] := 1;

• • collatz[x_ ? EvenQ] := x / 2;

• • collatz[x_] := 3 x + 1;

• • list = FixedPointList[collatz, 14]

Plot this:

• • ListLinePlot[list]