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SATURDAY, MAY 28, 2016
If you've ever been a child, chances are you know a thing or too about Voronoi diagrams. And chances are, you've been a child. Children, it seems are the champions of Voronoi diagrams - aware of the most subtle rules that we adults are oft to forget. Shadows, for example, are an important part of Voronoi Diagrams - which has given rise to the term "Shadowing."

But perhaps I'm getting ahead of myself. Even if you've experienced and knew everything there was to know about Voronoi diagrams, it's entirely likely you didn't know it under that name. Instead, you referred to it as your "space." So let me take a moment and formerly define a Voronoi Diagram then: If you were to scatter points randomly on a plain, a point's "space" would consist of the area that's closer to the point, than any other.1

An example of a Voronoi Diagram

With randomly scattered points, this can make for some interesting diagrams. For more orderly scattered points - points in a classroom, for example, this leads to roughly more rectangular shapes. These spaces are guarded and defended with everything at a child's disposal. And thus, when an object in another's space is casting a shadow upon their own space, ie. the aforementioned "shadowing," great wars are waged.

I recall long road trips with my brother in which our parents would intervene on our bickering by forming physical barriers to illustrate the Voronoi diagram boundaries. Confined to our spaces, we were suddenly overwhelmed with claustrophobia, which thrust us into another disagreement - who has more area within their zone, or who has more "land." There would be no peace for my parents.

It's interesting that as adults, we encourage children to destroy the concept of these Voronoi diagrams, and allow for some overlapping. "Share," we tell them. And many adults spend countless hours in single bars, or on the internet, searching for that special someone who is willing to share a Voronoi Cell. We invite friends over and encourage them to be partake upon the special items we've filled our Voronoi cells with. And yet, somehow while so encouraging upon children of sharing their Voronoi cells, and also leading by example in sharing ours - we get to a point where we, as a collective, don't want our space shared. Actual wars are waged, endless battles, over that same issue of who has more area within their space, as well as ensuring no one enters our collective cells unannounced. Odd that when we consider our personal cells, we are so open and welcoming with them - but the addition of the other cells, cells which do not belong to us, but whose owners we feel are similar to us in nature, the mere consideration of our cell as part of this larger set of cells, builds this fire in our bellies.

A Voronoi Diagram after borders were shifted for political reasons

And so we create physical barriers, outlining our Voronoi cells, and instill a fear in others to encourage them to protect our walls, warning them of the imminent threat of others who are Shadowing on our space.



Voronoi cells inside of Voronoi cells inside of even more Voronoi cells, such as rooms inside of houses inside of countries, makes for an interesting understanding of sharing and space. I've never thought of sharing a desk in school like this, and how its simuliar to the sharing of countries side by sides starting a lot bigger wars than me and a classmate bickering.

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