Jason Cawley
Wolfram Science Group
Phoenix, AZ USA
Registered: Aug 2003
Posts: 712 
If you have Mathematica 6, you can program this system and display the results, interactively, in two lines, as follows 
SinFract[start_, anglefactor_, angleadd_, steps_] := NestList[Sin[# * anglefactor + angleadd] &, start, steps]
Manipulate[ ListLinePlot[SinFract[start, anglefactor, angleadd, steps], PlotMarkers > Automatic, AxesOrigin > {0, 0}, Frame > True, PlotRange > All], {{start, 0.9}, 1, 1}, {{anglefactor, 1.3}, .5, 6.3}, {{angleadd, .1}, [Pi]/2, [Pi]/2}, {{steps, 10}, 1, 100, 1}]
The first line is your function, with four parameters. NestList says do this nestedly steps times and leave a trail of the results.
The second line creates an interactive plot with controls for your variables on "sliders".
Even if you don't have Mathematica 6 to make this sort of illustration in a few minutes, you can still use the result, because I used our new "Publish for Player" feature, here 
http://www.wolfram.com/solutions/in...oyment/publish/
You can get Mathematica Player, free, from this link 
http://www.wolfram.com/products/player/download.cgi
I will attach this specific interactive notebook below. All you need is Player to use it.
It is a reasonably interesting little system, incidentally. It reminds me closely of the kneading route to chaos system described on 307 of the NKS book. The whole section starting at page 304 is relevant.
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