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Dynamics activity "drainage"

• To: mathgroup at smc.vnet.net
• Subject: [mg123503] Dynamics activity "drainage"
• From: Chris Young <cy56 at comcast.net>
• Date: Fri, 9 Dec 2011 05:56:25 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

The plot at the bottom (with ParametricPlot3D) won't appear after 5 
minutes, at which point I aborted it. I've got a definition of f 
earlier in the file, but I can't figure out why I get a warning about 
"potentially harmful dynamic activity" (or something like that) when I 
open the file.

There's a notebook at http://home.comcast.net/~cy56/ComplexPlotProbs.nb
and a picture at http://home.comcast.net/~cy56/ComplexPlotProbs.png 
showing the constant yellow highlighting of the selection bar.

Chris Young
cy56 at comcast.net

Clear[f];

f[1][z_] := z;
f[2][z_] := 3 Re[z] + 2 Im[z] I;
f[3][z_] := Cos[z];
f[4][z_] := Sin[z];

f[5][z_] := z^2;
f[6][z_] := (3 Re[z] + 2 Im[z] I)^2;
f[7][z_] := Cosh[z];
f[8][z_] := Sinh[z];

The following plots, but the selection bar to the right of the plot 
stays highlighted. Is some kind of evaluation going on all the time? 
Should I have the functions in a DynamicModule?

Manipulate[
 GraphicsGrid[
  Partition[
   Table[
    ContourPlot3D[
     z == Abs[f[k][x + y I]],
     {x, -\[Pi], \[Pi]}, {y, -\[Pi], \[Pi]}, {z, 0, 2 \[Pi]},

     AxesLabel -> {"x", "y", "z"},
     PlotRange -> {{-\[Pi], \[Pi]}, {-\[Pi], \[Pi]}, {0, 2 \[Pi]}},
     PlotPoints -> plotPts,
     BoxRatios -> 1,
     Mesh -> 12,
     MeshFunctions -> {
       ( {x, y} \[Function] Arg[f[k][x + y I]])
       },
     ColorFunctionScaling -> False,
     ColorFunction -> ({x, y} \[Function]
        Hue[\[LeftFloor]12 (Arg[f[k][x + y I]] + \[Pi])/(
           2 \[Pi])\[RightFloor]/12, 0.5, 1])
     ],
    {k, 1, 8}
    ],
   4
   ],
  ImageSize -> Large
  ],
 {{plotPts, 30}, 10, 50, 5}
 ]


Manipulate[
 GraphicsGrid[
  Partition[
   Table[
    ParametricPlot3D[
     {x, y, Abs[f[k][x + y I]]},
     {x, -\[Pi], \[Pi]}, {y, -\[Pi], \[Pi]},

     AxesLabel -> {"x", "y", "z"},
     PlotRange -> {{-\[Pi], \[Pi]}, {-\[Pi], \[Pi]}, {0, 2 \[Pi]}},
     PlotPoints -> plotPts,
     BoxRatios -> 1,
     Mesh -> 12,
     MeshFunctions -> {
       ( {x, y} \[Function] Arg[f[k][x + y I]])
       },
     ColorFunctionScaling -> False,
     ColorFunction -> ({x, y} \[Function]
        Hue[\[LeftFloor]12 (Arg[f[k][x + y I]] + \[Pi])/(
           2 \[Pi])\[RightFloor]/12, 0.5, 1])
     ],
    {k, 1, 8}
    ],
   4
   ],
  ImageSize -> Large
  ],
 {{plotPts, 30}, 10, 50, 5}
 ]