[Press here to see animation again!]

The animation was originally drawn using Maple:

> with(plots):
> animate({[s+cos(t), 1+sin(t), t=0..2*Pi],[t-sin(t), 1-cos(t),t=0..4*Pi],[s-t*sin(s), 1-t*cos(s), t=0..1]},s=0..4*Pi,frames=50,color=blue);

The graphs from this animation were then modified and combined together to form the above animation.