2012.10.30 Another map experiment: Voronoi states

Not letting another calendar year slide past without a single POIB post, unlike 2010! Here is an experiment with the geography of the U.S. states along similar lines as last year's border states. Rather than each new state comprising all points closer to a given state boundary than to any other state boundary, these states comprise all points closer to a given state capital than to any other state capital. That's right: this is a Voronoi decomposition of the Lower 48 using the state capitals as seeds. Because there's a state for every state capital, we can consider these new states reshaped versions of the existing lower 48 states. Click the map for a double-wide version, click again for the smaller version:

Voronoi U.S. states map

Some observations:

Here's a boiled-down explanation of how I constructed the map:

  1. Start with the US map with state capitals in Illustrator.
  2. Draw the Delaunay triangulation of the state capitals.
  3. For each line drawn, rotate it 90° about its center by shift+dragging the line via its rotation cursor (which shows up when hovering the cursor just offset from any corner of the line's selection box).
  4. Trim the lines at every place where three close-together lines (a badly inexact description) intersect, extending lines first where needed. Keep the part of the line that connects to another three-line intersection. Obviously.

That's it, basically! It sounds pretty arcane maybe when explained that way, but one gets the hang of it quickly with practice. It's fun! Trust me.

Bonus: here are the names of all the Voronoi states, in alphabetical order of their real counterparts: Vorobama, Vorlaska, Vorozona, Vorkansas, Calivornia, Vorolado, Voronnecticut, Delavore, Vlorida, Vorgia, Havoii, Voidoho, Villonoi, Vorondiana, Voronoiowa, Voronansas, Vorontucky, Vorisiana, Voronoine, Voryland, Voronassachusetts, Voronichigan, Voronnesota, Voronississippi, Voronissouri, Vorontana, Voronebraska, Nevorda, Noi Vorshire, Noi Vorsey, Noi Vorxico, Noi Vork, Vorth Carolina, Vorth Dakota, Vorhio, Vorklahoma, Voregon, Pennsylvornia, Vorde Island, South Caronoina, South Davorta, Voronnessee, Vorxas, Utonoi, Vormont, Vorginia, Vorshington, West Vorginia, Vorsconsin, Voronoyoming. Whew!