Re: Complex Plot

• To: mathgroup at smc.vnet.net
• Subject: [mg88310] Re: Complex Plot
• From: "Kevin J. McCann" <Kevin.McCann at umbc.edu>
• Date: Thu, 1 May 2008 03:21:50 -0400 (EDT)
• Organization: University System of Maryland
• References: <fv9a83\$mjo\$1@smc.vnet.net> <fv9jub\$55i\$1@smc.vnet.net>

```Chris,

I think Jean-Marc has what you need if you just use the Contours->{0}
option, then it will show you the answer. It is interesting that the
larger you make PlotPoints, the more solutions there are. There is
probably some sort of relationship to chaotic functions here. The code
below takes a while on my reasonably fast machine, Jean-Marc's original
code set PlotPoints to 500 and it took a really long time.

Kevin

Here is a slight mod on Jean-Marc's code:

ContourPlot[Sin[x^2 y] - Log[x/y], {x, -12, 35}, {y, -8, 23},
ImageSize -> 500, ContourShading -> None, ContourStyle -> Red,
MaxRecursion -> 0, PlotPoints -> 250, Contours -> {0},
FrameLabel -> {"x", "y"},
PlotLabel ->
"Contours of Sin[\!\(\*SuperscriptBox[\"x\", \"2\"]\) \
y]-Log[\!\(\*FractionBox[\"x\", \"y\"]\)] = 0",
BaseStyle -> {FontFamily -> "Arial", FontWeight -> Bold,
FontSize -> 14}, FrameStyle -> AbsoluteThickness[2]]

Jean-Marc Gulliet wrote:
> Chris Degnen wrote:
>
>> Can anyone tell me how I can re-express this
>> equation in terms of x for plotting?
>>
>> Sin[x^2*y]==Log[x/y]
>>
>> last sighted: http://tinyurl.com/3s4hfd
>
> Hi Chris,
>
> If you are interested in the graphical representation of this function,
> you may want to use *ContourPlot* and experiment with its various
> options. For instance,
>
> ContourPlot[Sin[x^2*y] - Log[x/y], {x, -12, 35}, {y, -8, 23},
>   ImageSize -> 500]
>
> ContourPlot[Sin[x^2*y] - Log[x/y], {x, -12, 35}, {y, -8, 23},
>   ImageSize -> 500, ColorFunction -> (White &), ContourStyle -> Black,
>   MaxRecursion -> 0, PlotPoints -> 500]
>
> You can see the result at
>
> http://homepages.nyu.edu/~jmg336/mathematica/chrisdegnencomplexplot.pdf
>
> Note that the second plot may take several minutes to complete due to
> the huge number of sampling points, but it should be very close to what
> you have seen on the Internet.
>
> Hope this helps,
> -- Jean-Marc
>

--

Kevin J. McCann
Research Associate Professor
JCET/Physics
Physics Building
University of Maryland, Baltimore County
1000 Hilltop Circle
Baltimore, MD 21250

```

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