WOLFRAM|DEMONSTRATIONS PROJECT

Tetration

​
view
density
contour
plot 3D
f
Re
Im
Abs
Arg
n
2
3
4
5
∞
points
15

Tetration (or a power tower) is iterated exponentiation, defined as

n
z=
z
z
.
.
.
z
︸
n
,

where
z
is a complex number. It was first introduced by Reuben Louis Goodstein. The image above shows three views of
f(
n
z
) for four different choices of
f
.