Fractals/exponential

parameter space of the complex exponential family f(z)=exp(z)+c. The parameter in the middle of the picture is postsingularly preperiodic (PSP). Eight parameter rays landing at this parameter are drawn in black. The bifurcation locus is grey, while hyperbolic components are shown as colored regions. Escaping set of (exp x-1)/2. (Arnaud Cheritat)

Exponential maps [1][2]

How to compute it 

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

References

  1. ↑ Dynamics of exponential maps by Lasse Rempe
  2. ↑ wikipedia : Exponential map (discrete dynamical systems)
Last modified on 1 March 2013, at 16:32