Circle and Square

Voronoi Decomposition

From Wikipedia: “In mathematics, a Voronoi diagram is a special kind of decomposition of a metric space determined by distances to a specified discrete set of objects in the space, e.g., by a discrete set of points.”

Well, we all got that, didn’t we? It will be on next week’s quiz, for sure. Seriously though, the Voronoi decomposition on the left is an object of beauty. Minus the little dots, of course, which you will definitely notice if you click to enlarge. These points determine the decomposition. The artistic effect is better when they are eliminated. But here is the deal. Focus on one of those dots. Focus next on the “cell” containing the dot. How is it defined? Well, it is the set of points that is closer to that dot than to any other dot. Folks, that’s math! We snuck it in under the radar!! Fun wasn’t it?

For more info see the Wikipedia articles: Voronoi Diagrams, Delaunay Triangulations. See also: Image Credits. In the credits you will find a C program used to create the image, and in the program you will find an unusual Biblical reference of the numerological kind.

zipTimer: an iPod/iPhone app for pacing piano practice, workouts, you name it.