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How to plot field lines of conformal mapping

  • To: mathgroup at
  • Subject: [mg26083] How to plot field lines of conformal mapping
  • From: Jos R Bergervoet <Jos.Bergervoet at>
  • Date: Tue, 28 Nov 2000 01:55:29 -0500 (EST)
  • Organization: Philips Research Laboratories
  • Sender: owner-wri-mathgroup at

I would like to plot a family of field lines obtained from a conformal
mapping, as in the following code snippet. Is there a shorter way?

  f = z + I Sinh[z]

                    {Re[f], Im[f]} /. z->u-Pi/2I,
                    {Re[f], Im[f]} /. z->u-1.5I,
                    {Re[f], Im[f]} /. z->u-1.25I,
                    {Re[f], Im[f]} /. z->u-1.0I,
                    {Re[f], Im[f]} /. z->u-0.75I,
                    {Re[f], Im[f]} /. z->u-0.5I,
                    {Re[f], Im[f]} /. z->u-0.25I,
                    {Re[f], Im[f]} /. z->u+0I,
                    {Re[f], Im[f]} /. z->u+0.25I,
                    {Re[f], Im[f]} /. z->u+0.5I,
                    {Re[f], Im[f]} /. z->u+0.75I,
                    {Re[f], Im[f]} /. z->u+1.0I,
                    {Re[f], Im[f]} /. z->u+1.25I,
                    {Re[f], Im[f]} /. z->u+1.5I,
                    {Re[f], Im[f]} /. z->u+Pi/2I
                    {u,-3,3}, PlotPoints->700]

I tried (without success) to do it after creating a table in advance:

  n = 1
  t = Table[{Re[f], Im[f]} /. z->u+i/n Pi/2I , {i, -n,n}]
  ParametricPlot[t, {u,-3,3}, PlotPoints->700]

This does not work. Does anyone know an elegant solution?

NB: I do not want the full CartesianMap[F , {-3,3}, {-Pi/2,Pi/2}]
but only one of the two families of lines.

Thanks in advance,

  Dr. Jozef R. Bergervoet                      Electromagnetism and EMC
  Philips Research Laboratories,             Eindhoven, The Netherlands
  Building WS01                                     FAX: +31-40-2742224
  E-mail: Jos.Bergervoet at              Phone: +31-40-2742403

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