This Demonstration displays nearest neighbor tours (use the step slider to see them) along with a better tour computed by the built-in Mathematica function FindShortestTour, forming the outline of the blue polygon. All nearest neighbor tours start at point 1.

There is a moment at which some points are "forgotten" during the course of the algorithm, and they have to be inserted at a great cost in the end. Though usually rather bad, nearest neighbor tours have the advantage that they only contain a few severe mistakes while being very fast and easy to implement. Therefore, such tours can serve as good starting tours that other methods can improve.