Infinite tetration giving I*Omega costant=I*0.567143...

[bo198214]

Of course, its 4D, that is needed. So we either need to know where to look for projection to 3D, or have some mapping that reduces dimensionality ( if there is one).

Yes, if you look at wikipedia or mathworld for example for the Lambert W function you get plots of the real and imaginary part and of the absolute value of the function in dependence on the complex argument (in the horizontal plane).

I need to add few more formulae and check before we can explain(? ) oscillations related to Omega and W(1),I mentioned in another thread :

Omega^(1/(I*Omega) = e^I

Omega^(-1/(I*Omega)=e^-I

sin (z) = (-I/2)* (Omega^(z/(I*Omega))-Omega^(-z/(I*Omega)))

cos (z) = (1/2)*((Omega^(z/(I*Omega))+Omega^(-z/(I*Omega)))

But Ivars you can show that on your own, its quite similar to the derivation in my previous post (if you use the reply button you can even see the tex source and learn how to write things nicer with tex).