       Re: How to plot field lines of conformal mapping

• To: mathgroup at smc.vnet.net
• Subject: [mg26171] Re: [mg26083] How to plot field lines of conformal mapping
• From: BobHanlon at aol.com
• Date: Thu, 30 Nov 2000 01:04:13 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```f = z + I Sinh[z];

Off[ParametricPlot::ppcom];

ParametricPlot[
Evaluate[
Join[{{Re[f], Im[f]} /. z -> u - Pi/2I},
Table[{Re[f], Im[f]} /. z -> u - x*I, {x, -1.5,
1.5, .25}], {{Re[f], Im[f]} /. z -> u - Pi/2I}]],
{u, -3, 3}, PlotPoints -> 700,
PlotStyle -> {RGBColor[1, 0, 0], RGBColor[0, 0, 1]}];

This can be simplified further if the curves are "uniformly" spaced

ParametricPlot[
Evaluate[
Table[{Re[f], Im[f]} /. z -> u - x*I, {x, -Pi/2, Pi/2, Pi/12}]],
{u, -3, 3}, PlotPoints -> 700,
PlotStyle -> {RGBColor[1, 0, 0], RGBColor[0, 0, 1]}];

Bob Hanlon

In a message dated 11/28/00 3:27:44 AM, Jos.Bergervoet at philips.com writes:

>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]
>
>  ParametricPlot[{
>                    {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.
>

```

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