Infinite tetration of the imaginary unit

[sheldonison]

what if b^^0 is large ?

im not sure if we get the same behaviour.

if b^^0 is large we might reach divergence ?

I don't understand -- but we observe what appears to be fractal behavior, (on the Shell-Thron boundary) which would be the edge of convergence.

....the area within the cycles is also of interest.

perhaps not usefull , but i always try to map a cycle to a unit circle and then back again.

this can be done because of the riemann mapping theorem.

then i try to see how fast the iterations cycle on the unit circle ;

The picture in the wiki is in the upper half of the complex plane, but it can be contactenated with its complex conjugate to make an enclosed region. Then this region could certainly be Riemann mapped onto a unit circle...
- Sheldon