Fun with Math

United States of Voronoi

California Bob reports:

I just learned about this. This is one of those things that's easy to see but difficult to describe.

Voronoi Cells

A Voronoi diagram partitions a plane around points or "seeds" within it.  It THINK it divides the area so that the boundaries are always halfway between one seed and the next closest seed.

The official description is, boundaries are drawn so that all points within that boundary, are closer to its seed, than to any other seed.

If each seed was a repelling magnet, would this describe the same boundaries?

Here [image at top] it's used to draw state boundaries around state capitals.