(*^

::[	frontEndVersion = "Macintosh Mathematica Notebook Front End Version 2.1";
	macintoshStandardFontEncoding; 
	paletteColors = 128; automaticGrouping; currentKernel; 
	fontset = title, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e8,  24, "Times"; ;
	fontset = subtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e6,  18, "Times"; ;
	fontset = subsubtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, italic, e6,  14, "Times"; ;
	fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M22, bold, a20,  18, "Times"; ;
	fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M19, bold, a15,  14, "Times"; ;
	fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, bold, a12,  12, "Times"; ;
	fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; ;
	fontset = smalltext, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  10, "Times"; ;
	fontset = input, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeInput, M42, N23, bold, L-5,  12, "Courier"; ;
	fontset = output, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5,  12, "Courier"; ;
	fontset = message, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, R65535, L-5,  12, "Courier"; ;
	fontset = print, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5,  12, "Courier"; ;
	fontset = info, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, B65535, L-5,  12, "Courier"; ;
	fontset = postscript, PostScript, formatAsPostScript, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeGraphics, M7, l34, w282, h287,  12, "Courier"; ;
	fontset = name, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, italic,  10, "Geneva"; ;
	fontset = header, inactive, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; ;
	fontset = leftheader, inactive, L2,  12, "Times"; ;
	fontset = footer, inactive, noKeepOnOnePage, preserveAspect, center, M7,  12, "Times"; ;
	fontset = leftfooter, inactive, L2,  12, "Times"; ;
	fontset = help, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  10, "Times"; ;
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	fontset = special4, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7,  12, "Times"; ;
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]
:[font = special1; inactive; preserveAspect; ]
                 Sequences -- Period-Doubling and the Road to Chaos

The following cell shows how to generate one frame of a movie like the first movie in the browser window.  Evaluate it now.
;[s]
4:0,1;67,0;176,2;192,0;193,-1;
3:2,13,9,Times,0,12,0,0,0;1,13,9,Times,1,12,0,0,0;1,13,9,Times,1,12,65535,0,0;
:[font = input; preserveAspect; ]
Clear[Fcn, a, pop]

Fcn[p_] := a (1 - 0.01 p) p
pop[1] := 1
pop[n_] := pop[n] = Fcn[pop[n-1]]

a := 2.5

ListPlot[Table[{n, pop[n]}, {n, 1, 20}],
         PlotRange -> {0, 100},
         PlotJoined -> True]
:[font = special1; inactive; preserveAspect; ]
The next cell generates 30 frames for the first movie in the browser window.  Evaluate it now.
;[s]
3:0,0;78,1;94,0;95,-1;
2:2,13,9,Times,0,12,0,0,0;1,13,9,Times,1,12,65535,0,0;
:[font = input; preserveAspect; ]
For[a = 1.0; i = 0, 
    i <= 30, 
    i = i + 1; a = a + 0.1,
    Clear[pop];
    pop[1] = 5;
    pop[n_] := pop[n] = Fcn[pop[n - 1]];
    ListPlot[Table[{n, pop[n]}, {n, 1, 20}],
             PlotRange -> {0, 100},
             PlotJoined -> True]]
:[font = special1; inactive; preserveAspect; ]
Now you can view this movie by selecting the frames generated above and then choosing  Animate  Selected Graphics  from the Graph menu.  You can adjust the rate at which the movie is played by choosing  Animate  from the Graph menu.  Play the movie now.
;[s]
11:0,0;87,1;113,0;124,1;129,0;203,1;210,0;221,1;226,0;234,2;252,0;254,-1;
3:6,13,9,Times,0,12,0,0,0;4,13,9,Times,1,12,0,0,0;1,13,9,Times,1,12,65535,0,0;
:[font = special1; inactive; preserveAspect; ]
The next cell generates one frame of the second movie in the browser window.  Evaluate it now. 
;[s]
3:0,0;78,1;94,0;96,-1;
2:2,13,9,Times,0,12,0,0,0;1,13,9,Times,1,12,65535,0,0;
:[font = input; preserveAspect; ]
Clear[Fcn, a]

Fcn[p_] := a (1 - 0.01 p) p

a := 2.5

Plot[{p, Fcn[p], Fcn[Fcn[p]]},
     {p, 0, 100},
     AspectRatio -> Automatic,
     PlotRange -> {0, 100},
     PlotStyle ->
       {{RGBColor[0,0,0]}, 
        {RGBColor[1,0,0]},
        {RGBColor[0,0,1]}}]
:[font = input; preserveAspect; ]
For[a = 1.0; i = 0, 
    i <= 30, 
    i = i + 1; a = a + 0.1,
    Plot[{p, Fcn[p], Fcn[Fcn[p]]},
         {p, 0, 100},
         AspectRatio -> Automatic,
         PlotRange -> {0, 100},
         PlotStyle ->
           {{RGBColor[0,0,0]}, 
            {RGBColor[1,0,0]},
            {RGBColor[0,0,1]}}]]
:[font = special1; inactive; preserveAspect; ]
Now you can view this movie by selecting the frames generated above and then choosing  Animate  Selected Graphics  from the Graph menu.  You can adjust the rate at which the movie is played by choosing  Animate  from the Graph menu.  Play the movie now.
;[s]
11:0,0;87,1;113,0;124,1;129,0;203,1;210,0;221,1;226,0;234,2;252,0;254,-1;
3:6,13,9,Times,0,12,0,0,0;4,13,9,Times,1,12,0,0,0;1,13,9,Times,1,12,65535,0,0;
^*)