VectorFieldPlots`
VectorFieldPlots`

PolyaFieldPlot

As of Version 7.0, PolyaFieldPlot has been superseded by VectorPlot.

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.

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.

Examples

Basic Examples(1)

Polya field plot of :

Wolfram Research (2008), PolyaFieldPlot, Wolfram Language function, https://reference.wolfram.com/language/VectorFieldPlots/ref/PolyaFieldPlot.html.

Text

Wolfram Research (2008), PolyaFieldPlot, Wolfram Language function, https://reference.wolfram.com/language/VectorFieldPlots/ref/PolyaFieldPlot.html.

CMS

Wolfram Language. 2008. "PolyaFieldPlot." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/VectorFieldPlots/ref/PolyaFieldPlot.html.

APA

Wolfram Language. (2008). PolyaFieldPlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/VectorFieldPlots/ref/PolyaFieldPlot.html

BibTeX

@misc{reference.wolfram_2024_polyafieldplot, author="Wolfram Research", title="{PolyaFieldPlot}", year="2008", howpublished="\url{https://reference.wolfram.com/language/VectorFieldPlots/ref/PolyaFieldPlot.html}", note=[Accessed: 25-April-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_polyafieldplot, organization={Wolfram Research}, title={PolyaFieldPlot}, year={2008}, url={https://reference.wolfram.com/language/VectorFieldPlots/ref/PolyaFieldPlot.html}, note=[Accessed: 25-April-2024 ]}