Saunders Graphic

Author

Eric W. Weisstein
December 2, 2003

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Graphics/SaundersGraphic.nb.

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

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

Examples

<<Utilities`Plot`
<<Utilities`Typesetting`

Base-2

MakeBoxes[title[{b_,d_},f_],TraditionalForm]:=RowBox[{RowBox[{"b","=",b}],","," ",RowBox[{"d","=",d}],",",MakeBoxes[f,TraditionalForm]}]

Show[GraphicsArray[Block[{$DisplayFunction=Identity},
Table[
Flatten[Outer[DensityPlot[
RealDigits[#2[#1[x+I y]],2,2,-n][[1,1]],{x,-Pi,Pi},{y,-Pi,Pi},
PlotPoints->250,Mesh->False,ColorFunction->GrayLevel,
Compiled->False,
PlotLabel->TraditionalForm[title[{2,n},#2[#1[z]]]],FrameLabel->TraditionalForm/@{x,y}]&,{Sin,Cos},{Re,Im}]],
{n,3}]
]],ImageSize->500,GraphicsSpacing->0]//Timing

Show[GraphicsArray[Block[{$DisplayFunction=Identity},
Table[
Flatten[Outer[DensityPlot[
RealDigits[#2[#1[x+I y]],2,2,-n][[1,1]],{x,-Pi,Pi},{y,-Pi,Pi},
PlotPoints->250,Mesh->False,ColorFunction->GrayLevel,
Compiled->False,
FrameLabel->TraditionalForm/@{x,y}]&,{Sin,Cos},{Re,Im}]],
{n,3}]
]],ImageSize->500,GraphicsSpacing->0]//Timing

Base-10

Show[GraphicsArray[Block[{$DisplayFunction=Identity},
Table[
Flatten[Outer[DensityPlot[RealDigits[#2[#1[x+I y]],10,2,-n][[1,1]],{x,-Pi,Pi},{y,-Pi,Pi},PlotPoints->250,Mesh->False,ColorFunction->Hue,
Compiled->False,
PlotLabel->TraditionalForm[title[{10,n},#2[#1[z]]]],FrameLabel->TraditionalForm/@{x,y}]&,{Sin,Cos},{Re,Im}]],
{n,3}]
]],ImageSize->500,GraphicsSpacing->0]//Timing

Show[GraphicsArray[Block[{$DisplayFunction=Identity},
Table[
Flatten[Outer[DensityPlot[RealDigits[#2[#1[x+I y]],10,2,-n][[1,1]],{x,-Pi,Pi},{y,-Pi,Pi},PlotPoints->250,Mesh->False,ColorFunction->Hue,
Compiled->False,
FrameLabel->TraditionalForm/@{x,y}]&,{Sin,Cos},{Re,Im}]],
{n,2}]
]],ImageSize->500,GraphicsSpacing->0]//Timing

DensityPlot[RealDigits[Re[Cos[x+I y]],10,2,-3][[1,1]],{x,-Pi,Pi},{y,-Pi,Pi},PlotPoints->750,Mesh->False,ColorFunction->Hue,
Compiled->False,FrameLabel->TraditionalForm/@{x,y}]//Timing