Mathematica provides state-of-the-art fully automated visualization of vector functions and data—suitable for representing flows, field lines and other vector fields of any complexity.
StreamPlot — make a stream plot from a vector field function
ListStreamPlot — make a stream plot from vector field data
VectorPlot — plot vectors from a vector field function
ListVectorPlot — plot vectors from vector field data
Vector + Scalar Visualization
StreamDensityPlot — superimpose plots of vector and scalar field functions
ListStreamDensityPlot — superimpose plots of vector and scalar field data
StreamPoints,
VectorPoints — number or placement of streamlines, vectors
StreamScale,
VectorScale — scale and size of streamlines, vectors
ColorFunction,
Mesh,
MeshFunctions — coloring, meshing, contouring, etc. for scalars
