The fractal nature of iterated ln(x) [Bandwidth warning: lots of images!]

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The fractal nature of iterated ln(x) [Bandwidth warning: lots of images!]

jaydfox Offline

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09/07/2007, 06:59 PM

For each iteration, the point closest to the fixed point corresponds to something around 0.35 or 0.4, probably close to 1/e. However, the point that interests me is the point tangent to a logarithmic spiral that glances each iteration on the way out. This point corresponds to 0.4890195613601270345796506844621354... if you exponentiate it back out to the real interval (0, 1).

~ Jay Daniel Fox

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The fractal nature of iterated ln(x) [Bandwidth warning: lots of images!] - by jaydfox - 09/07/2007, 06:42 PM

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

RE: The fractal nature of iterated natural logarithms - by jaydfox - 09/07/2007, 06:56 PM

RE: The fractal nature of iterated natural logarithms - by Gottfried - 09/07/2007, 08:15 PM

RE: The fractal nature of iterated natural logarithms - by jaydfox - 09/07/2007, 08:31 PM

RE: The fractal nature of iterated natural logarithms - by jaydfox - 09/07/2007, 06:59 PM

RE: The fractal nature of iterated natural logarithms - by bo198214 - 09/07/2007, 07:44 PM

RE: The fractal nature of iterated ln(x) [Bandwidth warning: lots of images!] - by jaydfox - 09/07/2007, 08:21 PM

RE: The fractal nature of iterated ln(x) [Bandwidth warning: lots of images!] - by jaydfox - 09/07/2007, 09:13 PM

RE: The fractal nature of iterated ln(x) [Bandwidth warning: lots of images!] - by jaydfox - 09/07/2007, 10:47 PM

RE: The fractal nature of iterated ln(x) [Bandwidth warning: lots of images!] - by bo198214 - 09/08/2007, 05:06 PM

RE: The fractal nature of iterated ln(x) [Bandwidth warning: lots of images!] - by jaydfox - 09/08/2007, 05:39 PM

RE: The fractal nature of iterated ln(x) [Bandwidth warning: lots of images!] - by jaydfox - 09/08/2007, 05:15 AM

RE: The fractal nature of iterated ln(x) [Bandwidth warning: lots of images!] - by Gottfried - 09/08/2007, 08:43 AM

RE: The fractal nature of iterated ln(x) [Bandwidth warning: lots of images!] - by jaydfox - 09/08/2007, 05:46 PM

RE: The fractal nature of iterated ln(x) [Bandwidth warning: lots of images!] - by bo198214 - 09/08/2007, 07:03 PM

RE: The fractal nature of iterated ln(x) [Bandwidth warning: lots of images!] - by jaydfox - 09/09/2007, 01:21 AM

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