09/06/2007, 07:21 AM

Hmm, my initial excitement has been dulled. It seems that, while the iterated natural logarithms of the real interval (0,1) do seem to converge on a fixed point, they do so in a very fascinating fractal manner. Unfortunately, this fractal convergence to the fixed point makes it difficult to identify the "correct" way to fractionally iterate. A straight line or complex spiral would be very straightforward, but this fractal isn't. This isn't to say that I've given up hope of getting some useful information here, but it's not nearly as simple as I'd hoped.

~ Jay Daniel Fox