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PolyaFieldPlot

PolyaFieldPlot[f, {x, xmin, xmax}, {y, ymin, ymax}]
generates a plot of the complex-valued function f in the complex plane using the Polya representation.
PolyaFieldPlot[f, {x, xmin, xmax, dx}, {y, ymin, ymax, dy}]
uses steps dx in real component x and steps dy in imaginary component y.
  • PolyaFieldPlot has the same options as Graphics, with the following additions and changes:
ColorFunctionNonea function to use for coloring the vectors by their magnitude
MaxArrowLengthNonelength of the largest vector to be drawn, applied after the ScaleFunction, but before the ScaleFactor
PlotPoints15the number of evaluation points in each direction
ScaleFactorAutomaticlinearly rescales the vectors so the longest vector is equal to this value; Automatic fits the vectors in the mesh, None eliminates the rescaling
ScaleFunctionNonea function to use for rescaling the magnitude of vectors
  • In the Polya representation the magnitude is scaled using ScaleFunction->(Log[#+1]&) and the negative of the imaginary part is used.
Needs["VectorFieldPlots`"]
Polya field plot of sin z:
In[2]:=
Click for copyable input
Out[2]=