Gauss Map

Author

Eric W. Weisstein
October 31, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/SpecialFunctions/GaussMap.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/GaussMap.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Plots

<<Utilities`Plot`

Off[Power::"infy"]

Real Line

Plot[1/z-Floor[1/z],{z,-2,2},PlotRange->All,PlotStyle->Red,PlotPoints->200,AxesLabel->TraditionalForm/@{x,f[x]}]

Complex Plane

ComplexPlot3D[1/z-Floor[1/z],{z,-1,1},ComplexPlotLabel->f[z],
PlotPoints->200]//Timing

ComplexContourPlot[1/z-Floor[1/z],{z,-1,1},ComplexPlotLabel->f[z],
PlotPoints->200]//Timing

Plot[FractionalPart[1/z],{z,-2,2},PlotRange->All,PlotStyle->Red,PlotPoints->200,AxesLabel->TraditionalForm/@{x,f[x]}]

ComplexPlot3D[FractionalPart[1/z],{z,-1,1},ComplexPlotLabel->f[z],
PlotPoints->200]//Timing

ComplexContourPlot[FractionalPart[1/z],{z,-1,1},
PlotPoints->200]//Timing

Show[GraphicsArray[
Block[{$DisplayFunction=Identity},
ContourPlot[Abs[#[1/(x+I y)]],{x,-1,1},{y,-1,1},
ColorFunction->Hue,PlotPoints->500,ContourLines->False]&/@{#-Floor[#]&,FractionalPart}
]],ImageSize->500]