Fractals/exponential

Exponential maps

tetration fractals

Baker domains

How to compute it

$Z=x+y*i$

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

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

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

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

"The function

 $e^{x}-1$ 

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: "

 $e^{0}-1=0$

Images

• commons Category:Exponential maps

See also

• Julia_and_Mandelbrot_sets_for_transcendental_functions by Gertbuschmann