about voronoi diagrams

In mathematics, a Voronoi diagram, named after Georgy Voronoi, also called a Voronoi tessellation, a Voronoi decomposition, or a Dirichlet tessellation (after Lejeune Dirichlet), 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.
In the simplest and most common case, in the plane, we are given a set of points S, and the Voronoi diagram for S is the partition of the plane which associates a region V(p) with each point p from S in such a way that all points in V(p) are closer to p than to any other point in S.

Here are some Voronoi diagrams i generated using a special software that generates voronoi cells using points that you place in a specific metric space.
In nature we can find voronoi fractals as we can see in this photo taken from http://www.flickr.com/photos/flight404/538133104/