> 
# maptime.ms
# Time Series For a 1-Dimensional map
# 
> maptime := proc(F, x0, splist,caption)
>    local x, xlast, iter1, iter2, s, k, range, points, pts, p1, p2,
>          skipiter, plotiter;
> 
>    # splist := [skip,plot,skip,plot,skip,plot,...]
> 
>    x := x0:
> 
>    iter1 := 0;
>    iter2 := 0;
>    for s from 1 to nops(splist)/2 do
>       skipiter := op(2*s-1,splist);
>       plotiter := op(2*s,splist);
>       iter1 := iter2 + skipiter;
>       iter2 := iter1 + plotiter;
> 
>       # skip iterations
> 
>       for k from 1 to skipiter do x := F(x); od:
> 
>       # collect points for plotting iterations
> 
>       points := array(1..plotiter+1);
>       for k from 1 to plotiter+1 do
>          points[k] := [iter1+k-1, x];
>          xlast := x;
>          x := F(x);
>       od:
>       pts := convert(points,list);
>       x := xlast; # so we begin next graph where we left off
>       range := iter1..iter2, 0..1;
>       p1 := plot(pts, range, color=RGB(0,0,0), style=LINE):
>       p2 := plot(pts, range, color=blue, symbol=BOX, style=POINT):
>       print(plots[display]([p1, p2],title=caption));
>    od;
> end:


> test := proc() local a, Q;
> Q := unapply(a*x*(1-x),x);
> a := 2.9: maptime(Q, 0.1, [0,30,0,30],`a=2.9`);
> a := 3.2: maptime(Q, 0.1, [0,30,0,30],`a=3.2`);
> a := 3.5: maptime(Q, 0.1, [0,30,1000,30],`a=3.5`);
> a := 3.56:maptime(Q, 0.1, [0,30,1000,30],`a=3.56`);
> a := 3.74:maptime(Q, 0.1, [0,30,1000,30],`a=3.74`);
> a := 3.84:maptime(Q, 0.1, [0,30,1000,30],`a=3.84`);
> a := 3.9: maptime(Q, 0.1, [0,30,1000,30,1000,30],`a=3.9`);
> end:
> #test();


# generate some figures for the logistic map
# 
> Q := x -> a*x*(1-x);

                        Q := x -> a x (1 - x)

> #interface(plotdevice=postscript, plotoutput= `maptime1.ps`); 
> a := 2.9: maptime(Q,0.1,[0,50],`a=2.9`);


> #interface(plotdevice=postscript, plotoutput= `maptime2.ps`); 
> a := 3.2: maptime(Q,0.1,[0,50],`a=3.2`);


> #interface(plotdevice=postscript, plotoutput= `maptime3.ps`);
> a := 3.84: maptime(Q,0.1,[0,60],`a=3.84`);


> #interface(plotdevice=postscript, plotoutput= `maptime4.ps`);
> a := 3.9: maptime(Q,0.1,[10000,100],`a=3.9`);


>