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Upgrading from:

VectorFieldPlots`

As of Version 7, the Vector Field Plotting Package has been integrated into the Wolfram System.

New system functions

VectorFieldPlot is now available as the built-in Mathematica function VectorPlot:

Version 6.0 << VectorFieldPlots`; VectorFieldPlot[{Sin[x], Cos[y]}, {x, 0, 2 Pi}, {y, 0, 2 Pi}]
Wolfram Language code: VectorPlot[{Sin[x], Cos[y]}, {x, 0, 2Pi}, {y, 0, 2Pi}]

VectorFieldPlot3D is now available as the built-in Mathematica function VectorPlot3D:

Version 6.0 << VectorFieldPlots`; VectorFieldPlot3D[{x, y, z}, {x, 0, 1}, {y, 0, 1}, {z, 0, 1}]
Wolfram Language code: VectorPlot3D[{x, y, z}, {x, 0, 1}, {y, 0, 1}, {z, 0, 1}]

The VectorHeads option has been superseded by the VectorStyle option to VectorPlot3D:

Version 6.0 << VectorFieldPlots`; VectorFieldPlot3D[{x, y, z}, {x, 0, 1}, {y, 0, 1}, {z, 0, 1}, VectorHeads -> False]
Wolfram Language code: VectorPlot3D[{x, y, z}, {x, 0, 1}, {y, 0, 1}, {z, 0, 1}, VectorStyle -> Arrowheads[0]]

The ColorFunction option to VectorFieldPlot and VectorFieldPlot3D has been superseded by the new VectorColorFunction option:

Version 6.0 << VectorFieldPlots`; VectorFieldPlot[{Sin[x], Cos[y]}, {x, 0, 2 Pi}, {y, 0, 2 Pi}, ColorFunction -> Hue]
Wolfram Language code: VectorPlot[{Sin[x], Cos[y]}, {x, 0, 2Pi}, {y, 0, 2Pi}, VectorColorFunction -> Hue]

Use the VectorPoints option to increase the number of evaluation points in the plot:

Version 6.0 << VectorFieldPlots`; VectorFieldPlot[{Sin[x], Cos[y]}, {x, 0, 2 Pi}, {y, 0, 2 Pi}, PlotPoints -> 20]
Wolfram Language code: VectorPlot[{Sin[x], Cos[y]}, {x, 0, 2Pi}, {y, 0, 2Pi}, VectorPoints -> 20]

GradientFieldPlot, GradientFieldPlot3D, HamiltonianFieldPlot, and PolyaFieldPlot can be replaced using the following definitions:

Version 6.0 << VectorFieldPlots`; GradientFieldPlot[Sin[x y], {x, 0, 1}, {y, 0, 1}]
Wolfram Language code: GradientFieldPlot[f_, {x_, xmin_, xmax_}, {y_, ymin_, ymax_}, opts : OptionsPattern[]] := VectorPlot[Evaluate[D[f, {{x, y}}]], {x, xmin, xmax}, {y, ymin, ymax}, opts]
Wolfram Language code: GradientFieldPlot[Sin[x y], {x, 0, 1}, {y, 0, 1}]
Version 6.0 << VectorFieldPlots`; GradientFieldPlot3D[x^2 + y^2 - z^2, {x, 0, 1}, {y, 0, 1}, {z, 0, 1}]
Wolfram Language code: GradientFieldPlot3D[f_, {x_, xmin_, xmax_}, {y_, ymin_, ymax_}, {z_, zmin_, zmax_}, opts : OptionsPattern[]] := VectorPlot3D[Evaluate[D[f, {{x, y, z}}]], {x, xmin, xmax}, {y, ymin, ymax}, {z, zmin, zmax}, opts]
Wolfram Language code: GradientFieldPlot3D[x ^ 2 + y ^ 2 - z ^ 2, {x, 0, 1}, {y, 0, 1}, {z, 0, 1}]
Version 6.0 << VectorFieldPlots`; HamiltonianFieldPlot[Sin[x y], {x, 0, 2 \[Pi]}, {y, 0, 2 \[Pi]}]
Wolfram Language code: HamiltonianFieldPlot[f_, {x_, xmin_, xmax_}, {y_, ymin_, ymax_}, opts : OptionsPattern[]] := VectorPlot[Evaluate@{D[f, {y}], -D[f, {x}]}, {x, xmin, xmax}, {y, ymin, ymax}, opts]
Wolfram Language code: HamiltonianFieldPlot[Sin[x y], {x, 0, 2π}, {y, 0, 2π}]
Version 6.0 << VectorFieldPlots`; PolyaFieldPlot[Sin[x + I*y], {x, -1, 1}, {y, -1, 1}]
Wolfram Language code: PolyaFieldPlot[f_, {x_, xmin_, xmax_}, {y_, ymin_, ymax_}, opts : OptionsPattern[]] := VectorPlot[Evaluate@{Re[f], -Im[f]}, {x, xmin, xmax}, {y, ymin, ymax}, VectorScale -> {Automatic, Automatic, Log[#5 + 1]&}, opts]
Wolfram Language code: PolyaFieldPlot[Sin[x + I * y], {x, -1, 1}, {y, -1, 1}]