Train Tracks

Let c be a simple closed curve around the middle and left hole. Let f = gh, where h interchanges the right and middle holes counterclockwise, and g interchanges the left and middle holes clockwise. The picture on the left shows the action of f^2 on c. The one on the right reveals its train track.

Trefoil Knot

The trefoil knot is the simplest knot there is. To get it, start with a rope, tie up the rope, then glue its endpoints.

Klein Bottle

Leaf of a foliation on the torus