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Any way to get gradient lines as well as contour lines?

• To: mathgroup at smc.vnet.net
• Subject: [mg129663] Any way to get gradient lines as well as contour lines?
• From: Chris Young <cy56 at comcast.net>
• Date: Sun, 3 Feb 2013 02:48:23 -0500 (EST)
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I'd like to be able to plot "gradient lines", i.e., lines of steepest
descent, on plots of functions of x and y, f(x, y). The contour lines
can be obtained via MeshFunctions, as in

Plot3D[Sin[x + y^2], {x, -3, 3}, {y, -2, 2}, MeshFunctions -> {#3 &},
Mesh -> 5].

I'd like all the lines at right angles to these contours.

There must be some way to use the gradient function and then integrate
to the get the gradient lines.

Maybe this is difficult to do, in general. Also, maybe in general the
"gradient lines" wouldn't be continuous.

But I wonder if it could be done for some simple examples.

Any suggestions appreciated.

Chris Young
cy56 at comcast.net

• Follow-Ups:
  • Re: Any way to get gradient lines as well as contour lines?
    • From: James Stein <mathgroup@stein.org>
  • Re: Any way to get gradient lines as well as contour lines?
    • From: Bob Hanlon <hanlonr357@gmail.com>