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
- References:
- Re: Mathematica equivalent complexplot
- From: "David Park" <djmp@earthlink.net>
- Re: Mathematica equivalent complexplot