(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 93849, 2752]*) (*NotebookOutlinePosition[ 94904, 2788]*) (* CellTagsIndexPosition[ 94860, 2784]*) (*WindowFrame->Normal*) Notebook[{ Cell[TextData[{ StyleBox[ "Tools for Analyzing Discrete Dynamical Systems:\nGraphical Analysis\n", TextAlignment->Center, AspectRatioFixed->True, FontFamily->"Times", FontSize->18], StyleBox["Written by Richard A. Holmgren\nlast modified July 20, 1996", TextAlignment->Center, AspectRatioFixed->True, FontFamily->"Times", FontWeight->"Plain"] }], "Input", TextAlignment->Center, AspectRatioFixed->True], Cell[TextData[{ StyleBox["\tThese programs were developed for use with the text ", Evaluatable->False, AspectRatioFixed->True], StyleBox["A First Course in Discrete Dynamical Systems, 2nd edition", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[ " by Richard A. Holmgren, which was published by Springer-Verlag in 1996. \ ", Evaluatable->False, AspectRatioFixed->True], StyleBox[ " Suggestions for improvement are gratefully accepted. Please contact \ Professor Holmgren at ", Evaluatable->False, AspectRatioFixed->True], StyleBox["rholmgre@alleg.edu", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Courier"], StyleBox[" with suggestions and comments. 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Graphics[\"<<>>\"]\ \>", "\<\ -Graphics-\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True]}, Open]]}, Open]], Cell[CellGroupData[{Cell[TextData["Graphical Analysis with Three Initial Points "], "Section", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ StyleBox[ "This program does graphical analysis with three initial points denoted ", Evaluatable->False, AspectRatioFixed->True], StyleBox["x0", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold"], StyleBox[", ", Evaluatable->False, AspectRatioFixed->True], StyleBox["x1", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold"], StyleBox[", and ", Evaluatable->False, AspectRatioFixed->True], StyleBox["x2", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold"], StyleBox[".", Evaluatable->False, AspectRatioFixed->True] }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{Cell[TextData[{ StyleBox[ "Clear[f,firstIt,lastIt,xmin,xmax,i,y];\nf[x_] := 3.7x(1-x)\n\nx0 = .1", AspectRatioFixed->True], StyleBox["\t", AspectRatioFixed->True, FontWeight->"Plain"], StyleBox[";\nx1 = .2", AspectRatioFixed->True], StyleBox["\t", AspectRatioFixed->True, FontWeight->"Plain"], StyleBox[";\nx2 = .3\t;\n\nfirstIt = 0;\nlastIt = 5;\n\nxmin = ", AspectRatioFixed->True], StyleBox["0", AspectRatioFixed->True, FontWeight->"Plain"], StyleBox[ ";\nxmax = 1;\n\n(* computations for first seed *)\n\ni = 0;\ny = N[x0];\ \n\nWhile[i < firstIt, y = f[y]; i++];\n\nClear[dataTable0];\ndataTable0 = \ {{y,y},{y,f[y]}};\n\nClear[pts0];\npts0 = {Point[{y,y}],Point[{y,f[y]}]};\n\n\ While[i < lastIt,\n\ty = f[y];\n\tAppendTo[dataTable0,{y,y}];\n\t\ AppendTo[dataTable0,{y,f[y]}];\n\tAppendTo[pts0,Point[{y,y}]];\n\t\ AppendTo[pts0,Point[{y,f[y]}]];\n\ti++];\n\t\n\ AppendTo[dataTable0,{f[y],f[y]}];\nAppendTo[pts0,Point[{f[y],f[y]}]];\n\n\ cobweb0 = ListPlot[dataTable0,PlotJoined -> True,\n\tPlotRange -> \ {{xmin,xmax},{xmin,xmax}},\n\tAspectRatio -> 1,\n\tPlotStyle->GrayLevel[.1],\n\ \tDisplayFunction -> Identity];\n\t\nClear[showpts0];\nshowpts0 = \ Graphics[{PointSize[.013],pts0}];\n\n\t\n(* computations for second seed *)\ \n\ni = 0;\ny = N[x1];\n\nWhile[i < firstIt, y = f[y]; i++];\n\n\ Clear[dataTable1];\ndataTable1 = {{y,y},{y,f[y]}};\n\nClear[pts1];\npts1 = \ {Point[{y,y}],Point[{y,f[y]}]};\n\nWhile[i < lastIt,\n\ty = f[y];\n\t\ AppendTo[dataTable1,{y,y}];\n\tAppendTo[dataTable1,{y,f[y]}];\n\t\ AppendTo[pts1,Point[{y,y}]];\n\tAppendTo[pts1,Point[{y,f[y]}]];\n\ti++];\n\n\ AppendTo[dataTable1,{f[y],f[y]}];\nAppendTo[pts1,Point[{f[y],f[y]}]];\n\n\ cobweb1 = ListPlot[dataTable1,PlotJoined -> True,\n\tPlotRange -> \ {{xmin,xmax},{xmin,xmax}},\n\tAspectRatio -> 1,\n\tPlotStyle->GrayLevel[.3],\n\ \tDisplayFunction -> Identity];\n\t\nClear[showpts1];\nshowpts1 = \ Graphics[{PointSize[.013],pts1}];\n\n\n\t(* computations for third seed *)\n\ \ni = 0;\ny = N[x2];\n\nWhile[i < firstIt, y = f[y]; i++];\n\n\ Clear[dataTable2];\ndataTable2 = 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