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 Iterating at fixed points of b^x bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 10/04/2007, 05:54 PM bo198214 Wrote:However I am not sure in the moment for which area A the first case applies. Surely $f^{\circ n}(z)\to\infty$ for each $z>a_2$ where $a_2$ is the upper fixed point and $f^{\circ n}(z)\to a$ for all other real $z$. So then I simply made a fractal of it: The more green the color is the more iterations $n$ does it take that $|f^{\circ n}(z)|>T$ (i.e. the slower it converges to $\infty$) and if it needs more than 10 iterations (i.e. probably it does not converge to infinity but to the lower fixed point) then the color is black. I chose $b=\sqrt{2}$, the presented rectangle is $[4\dots 12] \times [-3\dots 3]$, I made it with FractalExplorer. $T=170$     $T=500$     $T=1000000000$     We see that the convergence to infinity is really chaotic. « Next Oldest | Next Newest »

 Messages In This Thread Iterating at fixed points of b^x - by bo198214 - 09/08/2007, 10:02 AM The fixed points of e^x - by bo198214 - 09/08/2007, 10:34 AM The fixed points of b^x - by bo198214 - 09/08/2007, 11:36 AM RE: Iterating at fixed points of b^x - by jaydfox - 09/12/2007, 06:23 AM RE: Iterating at fixed points of b^x - by bo198214 - 09/12/2007, 09:54 AM RE: Iterating at fixed points of b^x - by GFR - 10/03/2007, 11:03 PM RE: Iterating at fixed points of b^x - by Gottfried - 10/04/2007, 06:53 AM RE: Iterating at fixed points of b^x - by bo198214 - 10/04/2007, 01:30 PM RE: Iterating at fixed points of b^x - by bo198214 - 10/04/2007, 05:54 PM RE: Iterating at fixed points of b^x - by Gottfried - 10/04/2007, 11:05 PM RE: Iterating at fixed points of b^x - by GFR - 01/31/2008, 03:07 PM

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