Web Diagram

Author

Eric W. Weisstein
October 28, 2003

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

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

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

Logistic Map

<<Utilities`Typesetting`

LogisticSegments[r_,x0_,its_]:=Module[
{l=NestList[r#(1-#)&,x0,its]},
Partition[Flatten[Transpose[{l,l}]],2,1]
]

p2=Partition[LogisticSegments[3.741,.2,10],2,1];

movie=Table[Plot[{3.741x(1-x),x},{x,0,1},PlotStyle->{{},Dashing[{.02}]},
Prolog->MapIndexed[{Hue[#2[[1]]/Length[p2]],Line[#]}&,Take[p2,i]],
Epilog->{Text[y==f[x]//TraditionalForm,{.88,1}],
Text[y==HoldForm[3.741x(x-1)]//TraditionalForm,{.5,1}]},
AspectRatio->Automatic,
AxesLabel->TraditionalForm/@{(Subscript[x, n]),(Subscript[x, n+1])}
],{i,Length[p2]}];

<<Utilities`GIF`;

Export[gifs<>"webdiagr.gif",movie]//Timing