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based on an earlier version of the Wolfram Language.
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GradientFieldPlot3D[f, {x, xmin, xmax}, {y, ymin, ymax}, {z, zmin, zmax}]
generates a three-dimensional plot of the gradient vector field of the scalar function f as a function of x, y and z.
GradientFieldPlot3D[f, {x, xmin, xmax, dx}, {y, ymin, ymax, dy}, {z, zmin, zmax, dz}]
uses steps dx, dy and dz in variables x, y and z respectively.
  • GradientFieldPlot3D has the same options as Graphics3D, with the following additions and changes:
ScaleFactorAutomaticthe scale of the vectors to the mesh; Max ensures that the largest vector fits in the mesh
ScaleFunctionNonefunction to rescale the length of vectors
MaxArrowLengthNonedetermines the largest vector to be drawn
ColorFunctionNonethe colors to use
VectorHeadsFalsewhether to draw vectors with heads
PlotPoints7number of evalution points in each direction
Gradient field of x^2+y^2-z^2 over the unit cube:
Click for copyable input