# Fractals/exponential

Exponential maps [1][2][3][4]

tetration fractals [5]

Baker domains [6][7]

# How to compute it

${\displaystyle Z=x+y*i}$

${\displaystyle \exp(Z)=e^{Z}}$

${\displaystyle \mathrm {Real(\exp(Z))} =\exp(x)\cos(y)}$

${\displaystyle \mathrm {Imag(\exp(Z))} =\exp(x)\sin(y)}$


# What is the continous iteration of ${\displaystyle e^{x}-1}$ ?

"The function

 ${\displaystyle e^{x}-1}$


is one of the simpler applications of continuous iteration. The reason why is because regular iteration requires a fixed point in order to work, and this function has a very simple fixed point, namely zero: "[8]

 ${\displaystyle e^{0}-1=0}$