Date: Feb 3, 2013 2:52 AM
Author: Christopher O. Young
Subject: Any way to get gradient lines as well as contour lines?

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