## Voronoi diagram of people enjoying a park

Starting with an overhead shot of people sitting out in the sun in NYC’s Bryant Park, Rod Bogart laid what’s called a Voronoi diagram on top of it. A Voronoi diagram is a way of mapping out areas where any point in a given area is closer to a seed point than it is to any other seed point. You can think of it as a sphere of influence…and in this case, you can see how the park-goers have organized themselves into having their own personal space. As Bogart says:

It’s fascinating to see the real world optimization problem of wanting to get a nice large patch of grass.

I often think about Voronoi diagrams when I get into an elevator.

I stand alone in the elevator, right in the middle, equidistant from the four walls. Before the doors close, a woman enters. Unconsciously, I move over to make room for her. We stand side by side with equal amounts of space between the two of us and between each of us and the walls of the elevator. On the 12th floor, a man gets on and the woman and I slide slightly to the side and to the back, maximizing the space that each of us occupies in the elevator. At the 14th floor, another man gets on. The man in front steps to the back center and the woman and I move slightly toward the front, forming a diamond shape that again maximizes each person’s distance from the elevator walls and the people next to them.