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 Pretty pictures. andydude Long Time Fellow Posts: 509 Threads: 44 Joined: Aug 2007 11/18/2009, 05:56 AM (This post was last modified: 11/18/2009, 06:18 AM by andydude.) (11/17/2009, 09:17 PM)bo198214 Wrote: Apart from that the pictures look good. What type of plot is it (conformal or contour?) and how is it encoded in colors? How did you compute the 4-roots? Hue[h, s, b] is Mathematica notation for Hue-Saturation-Brightness encoding of colors, I found this function here and used it in my own code: Code:PrettyHue[Indeterminate]     := Hue[1, 0, 0]; PrettyHue[z_] :=     Hue[N[Mod[Arg[z], 2Pi]/(2Pi)],       1/(1 + 0.3 Log[Abs[z] + 1]),       1 - 1/(1.1 + 5Log[Abs[z] + 1])]; The idea is that white = infinity, black = 0, and red = positive real, cyan/blue = negative real, and all other colors represent the angle of the complex number. Roughly speaking, if $z = r e^{i \theta}$, then $\theta$ determines the hue, and $r$ determines the brightness. I think it is a brilliant way to show complex functions. Much more "smooth" than a contour plot, in my opinion. Sorry I should have said more about each function. So back to the functions. TetraRoot00 is $f(z) = z^{1/z}$, sorry for the silly name. TetraRoot2 is $f(z) = \ln(z)/W(\ln(z))$, which requires a good CAS. TetraPow2 is $f(z) = z^z$, which is pretty easy to compute. TetraPow3 is $f(z) = z^{z^z}$, which is also easy to compute, but slow. TetraPow4 is $f(z) = z^{z^{z^z}}$, which was very slow (attached below). I am currently in the process of trying to work out the complex structure of TetraRoot3, or $f(z)$ such that ${}^{3}(f(z)) = z$. Its not as "simple" as TetraRoot2, because instead of branch cuts on the real axis, the branch cuts are away from the real axis, I believe you can see this where the zeros are in TetraPow3' and if the derivative is zero, then the inverse function (TetraRoot3) should have a singularity at that point, right? This is TetraPow3':     This is TetraPow4:     Attached Files Image(s) « Next Oldest | Next Newest »

 Messages In This Thread Pretty pictures. - by andydude - 11/17/2009, 07:51 PM RE: Pretty pictures. - by bo198214 - 11/17/2009, 09:17 PM RE: Pretty pictures. - by andydude - 11/18/2009, 05:56 AM RE: Pretty pictures. - by andydude - 11/18/2009, 05:59 AM RE: Pretty pictures. - by andydude - 11/18/2009, 06:12 AM

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