03/26/2008, 04:46 PM
As it seems that Ivars is too fearful of complex numbers. I give here the plot (1/e)[4]t by regular iteration at the lower fixed point (1/e is indeed in the range of bases \( e^{-e}\dots e^{1/e} \) where there a real fixed point exists) via the previously mentioned formula.
As we already discussed in the thread Tetration below 1 the values for non-integer iterations are supposed to be complex. So I give here the curve of (1/e)[4]t, t=0...7 in the complex plane. We see that (1/e)[4]0=1 and of course (1/e)[4]1=1/e\( \approx \)0.36, (1/e)[4]2=(1/e)^(1/e)\( \approx \)0.69, etc.
As we already discussed in the thread Tetration below 1 the values for non-integer iterations are supposed to be complex. So I give here the curve of (1/e)[4]t, t=0...7 in the complex plane. We see that (1/e)[4]0=1 and of course (1/e)[4]1=1/e\( \approx \)0.36, (1/e)[4]2=(1/e)^(1/e)\( \approx \)0.69, etc.
