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

︸

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

.

Enrique Zeleny