Fractals/exponential

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

tetration fractals [5]

Baker domains [6][7]

How to compute itEdit

 
 
  

 

What is the continous iteration of  ?Edit

"The function

   

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]

  

ImagesEdit

   

See alsoEdit

ReferencesEdit

  1. THE EXPONENTIAL MAP IS CHAOTIC: AN INVITATION TO TRANSCENDENTAL DYNAMICS by ZHAIMING SHEN AND LASSE REMPE-GILLEN
  2. Dynamics of exponential maps by Lasse Rempe
  3. wikipedia : Exponential map (discrete dynamical systems)
  4. Paper by N Fagella
  5. Paul Bourke fractals tetration
  6. On the Stability of Julia Sets of Functions having Baker Domains by Arnd Lauber ( 2004)
  7. Approximation of Baker domains and convergence of Julia sets by Tania Garfias-Macedo aus Mexiko Stadt, Mexiko
  8. Tetration FAQ by Henryk Trappman Andrew Robbins July 10, 2008