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MathGroup Archive 2005

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Re: Re: Mathematica equivalent complexplot

  • To: mathgroup at smc.vnet.net
  • Subject: [mg57879] Re: [mg57845] Re: Mathematica equivalent complexplot
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Sat, 11 Jun 2005 03:35:34 -0400 (EDT)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <200506100629.CAA15577@smc.vnet.net>
  • Reply-to: murray at math.umass.edu
  • Sender: owner-wri-mathgroup at wolfram.com

I'm not sure the original poster just wanted to plot a curve in the 
complex plane (as implemented by the two methods you suggested); that's 
why I had raised the question of just what sort of graphical 
representation he expected.  After all, these plots represent merely the 
("static") range of function f and not the "mapping" from the reals to 
the complexes that f provides.

In principle, we should be able to represent that mapping since the 
total real dimension involved is 1 + 2 = 3; but I don't recall ever 
having seen such a graphical representation of such a mapping.  Perhaps 
the most appropriate thing would be to regard the input parameter x as 
time t, instead, and then to produce an animation showing evolution of 
the curve in time.

David Park wrote:
> Ron,
> 
> I think you are attempting to plot a curve in the complex plane. You can do
> it as follows.
> 
> Needs["Graphics`Colors`"]
> 
> f[x_] = Sin[x + I]
> I*Sinh[1 - I*x]
> 
> (Mathematica automatically transformed the Sin expression.)
> 
> ParametricPlot[{Re[f[x]], Im[f[x]]}, {x, -Pi, Pi},
>     AspectRatio -> Automatic,
>     PlotLabel -> SequenceForm["Curve ", f[x], " in Complex Plane"],
>     Frame -> True,
>     FrameLabel -> {"Re", "Im"},
>     FrameTicks -> Automatic,
>     Background -> Linen,
>     ImageSize -> 400];
> 
> For those who have the complex graphics package, Cardano3, from my web site
> below, there is a ComplexCurve routine (suggested by Murray Eisenberg).
> Cardano3 also requires DrawGraphics. Then the plot is done with...
> 
> Needs["Cardano3`ComplexGraphics`"]
> 
> ComplexGraphics[
>     {ComplexCurve[f[x], {x, -Pi, Pi}]},
>     PlotLabel -> SequenceForm["Curve ", f[x], " in Complex Plane"],
>     FrameLabel -> {"Re", "Im"},
>     FrameTicks -> Automatic,
>     Background -> Linen];
> 
> David Park
> djmp at earthlink.net
> http://home.earthlink.net/~djmp/
> 
> 
> From: raf . [mailto:arawak1 at yahoo.com]
To: mathgroup at smc.vnet.net
> 
> 
> This is a newbie question, I suppose. I've read as much as I can but cannot
> find a straight forward way to implement the complexplot in
> Mathematica 5.
> 
> An example call could be complexplot(sin(x+i),x=-Pi..Pi) where sin(x+i)
> is a typical function f(x) that maps real to complex and -Pi..Pi is the
> domain of f, a..b.  Of course, there are various plot options which can
> follow and would be included before the closing paren but I think I can
> handle that.
> 
> So any help would be appreciated.
> 
> Thanks much for the response.
> 
> Ron Francis
> 
> 
> 
> 

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


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