A relevant toy I threw together once to demonstrate finding a median/mean/centroid by minimizing a cost defined by "springs": http://www.cs.toronto.edu/~murray/

A relevant toy I threw together once to demonstrate finding a median/mean/centroid by minimizing a cost defined by "springs": http://www.cs.toronto.edu/~murray/04medoid/ http://www.cs.toronto.edu/~murray/04medoid/