2.86295 + 3.22327 i

[Gottfried]

Code:

b^b=b; b^L1=L1; b^L2=L2;
b=~2.8630+3.2233*I;  L1=~0.23429+0.72594*I;  L2=~-0.50419-1.0820*I;  
b=~3.7273+5.3180*I;  L1=~0.13364+0.66506*I;  L2=~-0.45567-0.86504*I;
b=~4.4332+7.1938*I;  L1=~0.08774+0.62923*I;  L2=~-0.42709-0.76959*I;

Kneser tetration plot for b=~2.8630+3.2233*I from -3+3i..+8-4i; generated using fatou.gp

When iterating exponentials, one tends to quickly get very large numbers or very small numbers.  In this plot, very small numbers have Tet(z)=~0 which is black, and then Tet(z+1)=~1; Red.  And Tet(z+2)=~2.8630+3.2233*I; Orangish.  Since its a repelling fixed point Tet(z+n) will eventually break away from the fixed point.
Continued Kneser tetration plot from +4+3i..+15-4i; Notice how the unstable fixed point takes over.  The white regions are large in magnitude and are seeds for super-exponential growth, but those regions are also unstable since when iterating large complex numbers half the time you go from very large to very small. 

Hi Sheldon - thanks for your remarks! Unfortunately I seem to have been "out-of-subject" ;-) too long: I don't get the relation of your graphic with the problem of zeros of z^z - z. Could you please explain further?