The fractal nature of iterated ln(x) [Bandwidth warning: lots of images!]
#2
The seventh iteration is the first to wrap back up towards \( \pi i \) as an upper asymptote:

   

But the 8th is the really interesting one:

   

Zooming in now, here's the 9th iteration:

   

Zooming in further, here's the 10th iteration (in yellow):

   

I get one more attachment for this post, so here's the 11th iteration at the same zoom:

   
~ Jay Daniel Fox
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RE: The fractal nature of iterated natural logarithms - by jaydfox - 09/07/2007, 06:46 PM

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