Standard Map

Author

Eric W. Weisstein
March 18, 2006

This notebook downloaded from http://mathworld.wolfram.com/notebooks/DynamicalSystems/StandardMap.nb.

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

©2006 Wolfram Research, Inc. except for portions noted otherwise

Code

StandardMap[k_,its_:100,cnt_:50]:=Graphics[{
Red,PointSize[.01],
Table[Point/@NestList[Mod[#[[2]]+k Sin[#[[1]]]+{#[[1]],0},2Pi]&,#,its]&[Table[2π Random[Real],{2}]],{cnt}]
},
PlotLabel->k,
AspectRatio->Automatic]

Figures

Show[GraphicsArray[Partition[Table[StandardMap[i],{i,0,3,.25}],4]],ImageSize->500]//Timing