2 x mod 1 Map

Author

Eric W. Weisstein
August 17, 2007

This notebook downloaded from http://mathworld.wolfram.com/notebooks/DynamicalSystems/2xmod1Map.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/2xmod1Map.html.

©2007 Wolfram Research, Inc. except for portions noted otherwise

Iterations

Factor[Table[Nest[Mod[2#,1]&,(Subscript[x, 0]),n],{n,3}]]//TableForm//TraditionalForm

Plots

<<Utilities`Typesetting`

GraphicsGrid[Partition[
Function[x0,ListPlot[Table[Nest[Mod[2#,1]&,x0,n],{n,50}],PlotRange->All,PlotStyle->Red,Joined->True,AxesLabel->{n,(Subscript[x, n])},PlotLabel->TraditionalForm[HoldForm[(Subscript[x, 0])]==x0],
PlotRange->{0,1},
ImageSize->200,
AxesOrigin->{0,0},
PlotRange->All]]/@{.1,.11,.111,.1111,.11111,FractionalPart[Pi],FractionalPart[E],FractionalPart[GoldenRatio]},4,4,{1,1},{}],Spacings->{-50,10},ImageSize->500]