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"Where The Buffalo Roamed" [] is a simple but persuading infographic illustrating the distance to the nearest McDonalds in the US.

This project required a lot of data, retrieved by AggData, a seemingly unique company focusing on providing original sets of quality data of all kinds (ranging from theComplete List of Victoria's Secret Locations for $39 to the Complete List of XBox Games for free). The data used for the map consisted of a complete list of about 13,000 geolocated U.S. restaurants.


There are none in West Virginia?

Fri 25 Sep 2009 at 4:31 AM

Nice visual, but can't you arrive at the same conclusions by simply using (apparently 107 mile radius) gradient plots of the locations of all US McDonald's? Seems more efficient to do that for 13K locations rather than computing the distance to the nearest McDonald's for each of almost 3M square miles (And common sense would suggest you could probably ignore all locations east of the Mississippi in the first place!)

Fri 25 Sep 2009 at 4:40 PM

@Erik: the trick is to compute the color of each pixel on the map. Drawing gradient (circle) plots around the 13K locations will result in overlapping areas where two or more circles collide. To prevent that, you need to know when to stop 'growing' your circles in one direction, eventually resulting in a so-called Voronoi-diagram. An inefficient O(n^2) but simple algorithm for that is iterate over all the points on the map and compute the minimum distance to each location.

Fri 25 Sep 2009 at 8:17 PM

Nice posting! Very interesting!

Greetings from Germany Julia

Sat 26 Sep 2009 at 12:13 AM

@JS I think the overlapping circles wouldn't be a problem here, if they were gradient and additive--we're really looking for the area with the least smount of overlap in the end. I would like to see a comparison of the two methods--maybe it's just two ways of getting to the same result.

Also, it seem like there is something a bit off about the shading in the graphic. (Yes, it's a cool effect--sort of like balloons or tomatoes being squished together) Maybe it's an optical illusion, but the dark areas between locations seem too dark, as other points equidistant from a location (but away from other stores) are shaded more brightly--though they are no closer to a location. So, intuitively, it seems like there should be more circular overlapping and less squishing.

Sat 26 Sep 2009 at 5:07 AM

I think this method, using gradients and the lighten blend mode in Photoshop, will achieve the Voronoi-diagram results J5 describes, using an approach similar to what Erik suggests (ie. no algorithm necessary, just a radial gradient emanating from each location).

Sat 26 Sep 2009 at 8:26 AM

@Mopkba - Yes, that is closer, but it looks like you still end up with a Voronoi diagram. Here is a page which coincidentally relates McDonald's locations to Voronoi diagrams:

"For each person living in a particular [Voronoi] cell, the defining McDonald's represents the closest place to get a Big Mac."

But while the Voronoi's boundaries will define the closest McDonald's location, the 3D Voronoi shading does not directly correlate to the distance to the closest McDonald's, and that is why you get the darker equidistant lines between two locations. That is my quibble--beside the seeming inefficient algorithm of making every "location find its store" rather than just letting each store radially project its accessibility to the locations.

Sorry for dragging this out so long...

Sat 26 Sep 2009 at 5:16 PM

Beautiful really. Amazing that in 2009 the east is more developed.

Which software was used to create this? R, perhaps?

Wed 07 Oct 2009 at 8:52 AM
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