Trefoil Knot
 
Maple 8 code:
 
with(plots):
TieKnot := proc(n :: posint)
    local i, t, curve, picts;
    curve := [-10*cos(t) - 2*cos(5*t) + 15*sin(2*t),
              -15*cos(2*t) + 10*sin(t) -2*sin(5*t),
               10*cos(3*t)]:
 
    picts := [seq(tubeplot(curve,t=0..2*Pi*i/n, 
              radius=3), i=1..n)];
    display(picts, insequence=true);
end;
TieKnot(48);
 
Comments: 
  1. Maple's tubeplot command draws a "tube" around a parametric curve--in this case, the curve for a trefoil knot.
  2. The image above was created with 48 frames.  You can experiment with other numbers of frames, as well as with various parametric curves and various values for the radius of the tube.
  3. An animation editor was used to slow down the display of the frames, as well as to add a 3-second display time to the final frame.
  4. This code was taken from p. 276 of the Maple 8 Advanced Programming Guide.