you will get a curve like a perfect bread! This is my chance
discovery.
And a bbs friend x8086 had given its 3d version:
f[\[Theta]_] := Nest[Sin, \[Theta], 1000]
ParametricPlot3D[{{f[\[Theta]] Cos[\[Theta]] Cos[\[Phi]],
f[\[Theta]] Cos[\[Theta]] Sin[\[Phi]],
f[\[Theta]] Sin[\[Theta]]}}, {\[Theta], 0, \[Pi]}, {\[Phi], 0,
2 \[Pi]}]
http://www.newsmth.net/bbstcon.php?board=Mathematics&gid=80561