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 Fractal behavior of tetration bo198214 Administrator Posts: 1,391 Threads: 90 Joined: Aug 2007 02/28/2009, 10:55 AM (This post was last modified: 02/28/2009, 11:01 AM by bo198214.) andydude Wrote:I suppose the Julia set of exponentiation would be the convergence region of ${}^{\infty}z$, right? By Wikipedia the Julia set of an entire function is Quote:the boundary of the set of points which converge to infinity under iteration For $\exp_b$ this would be the boundary of all points $x$ with $\lim_{n\to\infty} {\exp_b}^{\circ n}(x)=\infty$. I think for $b>e^{1/e}$ this is the whole complex plane, because the points that go to infinity are next to points that doent. For tetration the Julia set are is the boundary of points $x$ such that $\text{sexp}_b^{\circ n}(x)\to\infty$. I guess this depends on which tetration we choose. So maybe Dmitrii can draw a picture . Another option is the Mandelbrot set, which is the set of parameter $b$ for which $f_b^{\circ n}(0)\not\to\infty$, i.e. is bounded. « Next Oldest | Next Newest »

 Messages In This Thread Fractal behavior of tetration - by Kouznetsov - 01/28/2009, 03:38 AM RE: Fractal behavior of tetration - by bo198214 - 02/01/2009, 11:46 AM RE: Fractal behavior of tetration - by Kouznetsov - 02/01/2009, 06:44 PM RE: Fractal behavior of tetration - by andydude - 02/28/2009, 10:16 AM RE: Fractal behavior of tetration - by bo198214 - 02/28/2009, 10:55 AM

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