Rotating 3D Surface
 
Maple 8 code:
  
with(plots):
pic := n ->
    [plot3d(sin(sqrt(x^2+y^2)),x=-5..5,y=-5..5,
     orientation=[3*n,67],grid=[20,20])];
display(seq(pic(n),n=0..29),insequence=true);
 
Comments: 
  1. It is actually the viewpoint that is being rotated by this Maple code, rather than the surface.  However, the effect is that of the surface rotating in 3-space.
  2. The 4-way symmetry of this surface makes it possible to get by with rotating through only 90 degrees, rather than 360.  This results in a considerably smaller animated GIF file.  If you use a surface with less symmetry, you will have to rotate through a larger angle, resulting in more frames in the animation and a larger file size.
  3. Choose a color scheme in which the color of a point is determined by its z-coordinate; otherwise, there may be an abrupt color change when the rotation passes 90 degrees and starts again at 0 degrees.  To simplify the code, we selected the color (Z(Hue)) after Maple drew the graph.