VectorFieldPlots`

GradientFieldPlot

As of Version 7.0, GradientFieldPlot has been superseded by VectorPlot.

GradientFieldPlot[f,{x,x_min,x_max},{y,y_min,y_max}]

generates a plot of the gradient vector field of the scalar function f.

GradientFieldPlot[f,{x,x_min,x_max,dx},{y,y_min,y_max,dy}]

uses steps dx in variable x, and steps dy in variable y.

Details and Options

To use GradientFieldPlot, you first need to load the Vector Field Plotting Package using Needs["VectorFieldPlots`"].
The derivatives of f are calculated analytically.
GradientFieldPlot has the same options as Graphics, with the following additions and changes:

ColorFunction	None	a function to use for coloring the vectors by their magnitude
MaxArrowLength	None	length of the largest vector to be drawn, applied after the ScaleFunction, but before the ScaleFactor
PlotPoints	15	the number of evaluation points in each direction
ScaleFactor	Automatic	linearly rescales the vectors so the longest vector is equal to this value; Automatic fits the vectors in the mesh, None eliminates the rescaling
ScaleFunction	None	a function to use for rescaling the magnitude of vectors

Gradient field of over the unit square:

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