VectorFieldPlots`

PolyaFieldPlot

As of Version 7.0, PolyaFieldPlot has been superseded by VectorPlot.

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

generates a plot of the complex-valued function f in the complex plane using the Polya representation.

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

uses steps dx in real component x and steps dy in imaginary component y.

Details and Options

To use PolyaFieldPlot, you first need to load the Vector Field Plotting Package using Needs["VectorFieldPlots`"].
PolyaFieldPlot 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

In the Polya representation the magnitude is scaled using ScaleFunction->(Log[#+1]&) and the negative of the imaginary part is used.

Polya field plot of :

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