Harmonic Art
by pgroisma
A graph on the plane is a set of points linked by edges. If two points are linked we call them neighbors. Harmonic graphs are those that have the property that each point is exactly in the center (barycenter) of its neighbors. Harmonic graphs usually look “harmonic”, despite the name has nothing to do with this fact.
The pictures in this gallery are the outcome of research on harmonic random graphs. Given a random set of points in the plane we can construct a graph linking the points that are “close” to each other. Is it possible to deform this graph to turn it into a harmonic one without moving too much the points? The answer to this question has important consequences in probability theory and other fields. Pictures from the article Harmonic deformation of Delaunay triangulations
